Enter two sides and one angle, or three sides, to find the missing element of your triangle.
Length of side adjacent to angle B and opposite angle A.
Length of side adjacent to angle A and opposite angle B.
Length of the side opposite angle C (hypotenuse if right-angled).
Angle opposite side A (in degrees).
Angle opposite side B (in degrees).
Angle opposite side C (in degrees).
Calculation Results
Missing Side: —
Missing Angle: —
Intermediate Values:
Formula explanation will appear here.
Triangle Side and Angle Visualization
Triangle Properties
Property
Value
Side A
—
Side B
—
Side C
—
Angle A (α)
—
Angle B (β)
—
Angle C (γ)
—
Perimeter
—
Area
—
Understanding the Missing Side of Triangle Calculator
{primary_keyword} is a fundamental concept in geometry, essential for solving a wide array of problems in fields ranging from engineering and architecture to navigation and computer graphics. This {primary_keyword} calculator is designed to simplify the process of finding unknown dimensions or angles within a triangle when some information is already known. Whether you're a student grappling with trigonometry or a professional needing precise measurements, this tool and the accompanying guide will equip you with the knowledge to confidently tackle triangle calculations.
What is a Missing Side of Triangle Calculator?
A {primary_keyword} calculator is a specialized tool that uses trigonometric principles and geometric formulas to determine the length of a missing side or the measure of a missing angle in a triangle. Triangles are defined by three sides and three angles. If you know certain combinations of these elements, you can deduce the rest. This calculator helps automate those calculations, providing quick and accurate results.
Who should use it:
Students: Learning geometry, trigonometry, and pre-calculus.
Engineers & Architects: Designing structures, calculating loads, and ensuring stability.
Surveyors: Measuring land boundaries and distances.
Navigators: Determining positions and distances at sea or in the air.
Graphic Designers & Game Developers: Creating 2D and 3D models and environments.
DIY Enthusiasts: Planning projects involving angled cuts or measurements.
Common misconceptions:
"It only works for right-angled triangles." While right-angled triangles have specific, simpler formulas (like Pythagoras), this calculator is designed to handle any type of triangle (acute, obtuse, or right-angled) using more general laws like the Law of Sines and Law of Cosines.
"You always need angles." You can find a missing side if you know all three sides (using Heron's formula for area, then potentially the Law of Cosines to find angles if needed, though this calculator focuses on sides first). However, to find a *missing side* using the Law of Sines or Cosines, you typically need at least two sides and one angle, or specific combinations thereof.
"All triangles are the same." Triangles vary greatly in shape and size. The relationships between sides and angles are consistent, but the specific values change. This calculator accounts for these variations.
{primary_keyword} Formula and Mathematical Explanation
The calculation of a missing side or angle in a triangle relies on fundamental laws of trigonometry and geometry. The specific formula used depends on the information provided. The most common laws employed are the Law of Sines and the Law of Cosines.
1. Law of Sines:
This law relates the lengths of the sides of a triangle to the sines of its opposite angles. It's particularly useful when you know two angles and one side (AAS or ASA), or two sides and an angle opposite one of them (SSA – though this can sometimes lead to ambiguous cases).
The formula is:
a / sin(α) = b / sin(β) = c / sin(γ) = 2R
Where:
a, b, c are the lengths of the sides.
α, β, γ (or A, B, C) are the measures of the angles opposite those sides, respectively.
R is the radius of the triangle's circumcircle.
Derivation/Use Case: If you know sides a and b, and angle α, you can find angle β using sin(β) = (b * sin(α)) / a. Once you have two angles, you can find the third (since α + β + γ = 180°), and then use the Law of Sines again to find the remaining side c: c = (a * sin(γ)) / sin(α).
2. Law of Cosines:
This law is useful when you know two sides and the included angle (SAS), or all three sides (SSS). It relates the length of one side of a triangle to the cosine of the angle opposite it and the lengths of the other two sides.
The formulas are:
a² = b² + c² - 2bc * cos(α)
b² = a² + c² - 2ac * cos(β)
c² = a² + b² - 2ab * cos(γ)
Derivation/Use Case: If you know sides b and c, and the included angle α, you can directly calculate side a using the first formula. If you know all three sides (a, b, c), you can rearrange the formula to find an angle, for example, α:
cos(α) = (b² + c² - a²) / (2bc)
Then, α = arccos((b² + c² - a²) / (2bc)).
3. Sum of Angles:
The sum of the interior angles of any triangle is always 180 degrees.
α + β + γ = 180°
This is crucial for finding a missing angle when the other two are known.
4. Area Formulas:
While not directly for finding sides, area calculations can be intermediate steps.
Base and Height: Area = (1/2) * base * height
Heron's Formula (SSS): Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (s = (a+b+c)/2).
Trigonometric Formula (SAS): Area = (1/2)ab * sin(γ)
Variable Explanations
Triangle Variables
Variable
Meaning
Unit
Typical Range
Side (a, b, c)
Length of a triangle's side
Units of length (e.g., meters, feet, cm)
> 0
Angle (α, β, γ)
Measure of an interior angle
Degrees (°) or Radians (rad)
(0°, 180°) or (0, π)
Semi-perimeter (s)
Half the perimeter of the triangle
Units of length
> 0
Area
The space enclosed by the triangle
Square units (e.g., m², ft²)
> 0
Perimeter
The total length of all sides
Units of length
> 0
Practical Examples (Real-World Use Cases)
Let's illustrate how the {primary_keyword} calculator can be used with practical scenarios:
Example 1: Finding a Missing Side (SAS)
Scenario: An architect is designing a triangular patio. They know two sides measure 10 meters and 15 meters, and the angle between them (the included angle) is 70 degrees. They need to calculate the length of the third side to order the correct amount of paving material.
Inputs:
Side B = 10 m
Side C = 15 m
Angle A (α) = 70°
(Side A, Angle B, Angle C are unknown)
Calculation using Law of Cosines:
a² = b² + c² - 2bc * cos(α)
a² = 10² + 15² - 2 * 10 * 15 * cos(70°)
a² = 100 + 225 - 300 * 0.3420
a² = 325 - 102.6
a² = 222.4
a = sqrt(222.4) ≈ 14.91 m
Calculator Output: Missing Side (a) ≈ 14.91 m
Interpretation: The architect needs approximately 14.91 meters for the third side of the patio.
Example 2: Finding a Missing Angle (SSS)
Scenario: A surveyor is mapping a plot of land. They measure the three sides of a triangular section as 50 meters, 70 meters, and 90 meters. They need to determine the angles to draw an accurate map.
Inputs:
Side A = 50 m
Side B = 70 m
Side C = 90 m
(Angles A, B, C are unknown)
Calculation using Law of Cosines (to find Angle C):
c² = a² + b² - 2ab * cos(γ)
Rearranging for cos(γ):
cos(γ) = (a² + b² - c²) / (2ab)
cos(γ) = (50² + 70² - 90²) / (2 * 50 * 70)
cos(γ) = (2500 + 4900 - 8100) / 7000
cos(γ) = -700 / 7000 = -0.1
γ = arccos(-0.1) ≈ 95.74°
Calculator Output: Missing Angle (γ) ≈ 95.74°
Interpretation: The angle opposite the longest side (90m) is approximately 95.74 degrees. The surveyor can use this and subsequent calculations (e.g., using Law of Sines) to find the other angles.
How to Use This {primary_keyword} Calculator
Using the calculator is straightforward:
Identify Knowns: Determine which sides and angles of your triangle you already know. You need at least three pieces of information, with at least one side given, and specific combinations (like AAS, ASA, SAS, SSS).
Input Values: Enter the known values into the corresponding fields (Side A, Side B, Side C, Angle A, Angle B, Angle C). Ensure you use consistent units for lengths. Angles should be in degrees.
Select Calculation Mode (Implicit): The calculator automatically determines the appropriate formula (Law of Sines, Law of Cosines, or angle sum) based on the inputs provided. It prioritizes finding a missing side if possible, or a missing angle.
Click Calculate: Press the "Calculate" button.
Read Results: The calculator will display the primary result (missing side or angle) prominently. It will also show intermediate values, the formula used, and update the triangle properties table and visualization.
Interpret: Understand the calculated values in the context of your problem. For example, a calculated side length should be physically plausible given the other dimensions.
Reset: To start a new calculation, click the "Reset" button.
Copy: Use the "Copy Results" button to easily transfer the calculated data.
How to read results: The main result will clearly state whether a side or angle was calculated. Intermediate values show steps like calculating the semi-perimeter or intermediate trigonometric functions. The table provides a full summary of the triangle's properties.
Decision-making guidance: Ensure the calculated values make sense geometrically. For instance, the sum of any two sides must be greater than the third side (Triangle Inequality Theorem). Angles should sum to 180°. If you get an error or nonsensical result, double-check your inputs and ensure you've provided a valid combination of known values.
Key Factors That Affect {primary_keyword} Results
While the mathematical formulas are precise, several real-world factors and input considerations can influence the accuracy and applicability of the results:
Input Accuracy: The most significant factor. Measurement errors in the known sides or angles will directly propagate into the calculated results. Precise measurements are crucial for accurate outcomes.
Units of Measurement: Ensure all length inputs are in the same unit (e.g., all meters, all feet). The calculator will output the missing side in the same unit. Angles must be consistently in degrees (as specified by the calculator).
Triangle Inequality Theorem: For any valid triangle, the sum of the lengths of any two sides must be greater than the length of the third side (a + b > c, a + c > b, b + c > a). If this condition isn't met by the inputs, no triangle can be formed, and the calculator might produce errors or invalid results.
Ambiguous Case (SSA): When given two sides and a non-included angle (SSA), there might be zero, one, or two possible triangles. This calculator typically resolves to one solution based on standard trigonometric functions, but users should be aware of this potential ambiguity in certain geometric problems.
Angle Units (Degrees vs. Radians): The calculator is set to use degrees. Using radians without conversion will lead to incorrect results, as trigonometric functions behave differently based on the angle unit.
Rounding Precision: Calculations involving trigonometric functions often result in decimal values. The calculator applies a standard level of precision. For highly sensitive applications, consider the implications of rounding intermediate or final results.
Right-Angled vs. General Triangles: While this calculator handles general triangles, specific right-angled triangle properties (Pythagorean theorem) can sometimes be used as a shortcut or verification method if the triangle is known to be right-angled.
Data Validity: Ensure that the combination of inputs logically defines a unique triangle. For example, providing three angles without any side lengths is insufficient to determine specific side lengths.
Frequently Asked Questions (FAQ)
What information do I need to use the calculator?
You need at least three pieces of information about the triangle, including at least one side length. Common valid combinations include: two angles and one side (AAS or ASA), two sides and the included angle (SAS), or all three sides (SSS).
Can this calculator find all missing sides and angles?
If you provide enough valid information (typically 3 elements), the calculator will determine the remaining unknown elements. For example, if you input 3 sides, it can calculate all 3 angles. If you input 2 sides and an angle, it can find the remaining side and angles.
What happens if I enter invalid inputs?
The calculator includes inline validation. It will show error messages below the input fields for non-numeric values, negative lengths, or angles outside the valid range (0-180 degrees). It also checks for violations of the Triangle Inequality Theorem.
Does the calculator work for right-angled triangles?
Yes, the formulas used (Law of Sines and Cosines) are general and apply to all triangles, including right-angled ones. You can use it just like any other triangle, or you could potentially use simpler Pythagorean theorem calculations if you know it's a right triangle and have the right inputs.
What is the 'Ambiguous Case' (SSA)?
When you know two sides and an angle opposite one of them (SSA), there can sometimes be two different triangles that fit the given information. This calculator typically provides one valid solution based on standard trigonometric calculations. Be mindful of this if your problem context suggests multiple possibilities.
Can I calculate the area of the triangle?
While this calculator primarily focuses on sides and angles, the calculated properties table includes the area, derived using formulas like Heron's formula or the trigonometric area formula once all sides/angles are known.
What units does the calculator use?
Length inputs should be in any consistent unit (e.g., cm, inches, meters). The output for the missing side will be in the same unit. Angles must be entered in degrees.
How precise are the results?
The calculator uses standard floating-point arithmetic. Results are typically displayed with a reasonable number of decimal places. For extremely high-precision requirements, manual calculations or specialized software might be necessary.
Can I calculate the perimeter?
Yes, the 'Triangle Properties' table will display the calculated perimeter once all three sides are known or calculated.
var sideAInput = document.getElementById('sideA');
var sideBInput = document.getElementById('sideB');
var sideCInput = document.getElementById('sideC');
var angleAInput = document.getElementById('angleA');
var angleBInput = document.getElementById('angleB');
var angleCInput = document.getElementById('angleC');
var sideAError = document.getElementById('sideAError');
var sideBError = document.getElementById('sideBError');
var sideCError = document.getElementById('sideCError');
var angleAError = document.getElementById('angleAError');
var angleBError = document.getElementById('angleBError');
var angleCError = document.getElementById('angleCError');
var resultDiv = document.getElementById('result');
var missingSideResultSpan = document.getElementById('missingSideResult');
var missingAngleResultSpan = document.getElementById('missingAngleResult');
var intermediateValuesDiv = document.getElementById('intermediateValues');
var formulaExplanationP = document.getElementById('formulaExplanation');
var propSideATd = document.getElementById('propSideA');
var propSideBTd = document.getElementById('propSideB');
var propSideCTd = document.getElementById('propSideC');
var propAngleATd = document.getElementById('propAngleA');
var propAngleBTd = document.getElementById('propAngleB');
var propAngleCTd = document.getElementById('propAngleC');
var propPerimeterTd = document.getElementById('propPerimeter');
var propAreaTd = document.getElementById('propArea');
var chart = null;
var chartInstance = null;
function isValidNumber(value) {
return !isNaN(parseFloat(value)) && isFinite(value);
}
function clearErrors() {
sideAError.textContent = ";
sideBError.textContent = ";
sideCError.textContent = ";
angleAError.textContent = ";
angleBError.textContent = ";
angleCError.textContent = ";
}
function updatePropertiesTable(a, b, c, alpha, beta, gamma) {
propSideATd.textContent = formatValue(a);
propSideBTd.textContent = formatValue(b);
propSideCTd.textContent = formatValue(c);
propAngleATd.textContent = formatValue(alpha, true);
propAngleBTd.textContent = formatValue(beta, true);
propAngleCTd.textContent = formatValue(gamma, true);
var perimeter = '–';
var area = '–';
if (isValidNumber(a) && isValidNumber(b) && isValidNumber(c)) {
perimeter = (a + b + c).toFixed(3);
var s = (a + b + c) / 2;
if (s > a && s > b && s > c) { // Heron's formula condition
var areaCalc = Math.sqrt(s * (s – a) * (s – b) * (s – c));
if (!isNaN(areaCalc)) {
area = areaCalc.toFixed(3);
}
} else if (isValidNumber(a) && isValidNumber(b) && isValidNumber(alpha)) { // Area using SAS
var areaCalc = 0.5 * a * b * Math.sin(degreesToRadians(alpha));
if (!isNaN(areaCalc)) {
area = areaCalc.toFixed(3);
}
}
}
propPerimeterTd.textContent = perimeter;
propAreaTd.textContent = area;
}
function formatValue(value, isAngle = false) {
if (value === null || value === undefined || isNaN(value)) return '–';
if (isAngle) {
return value.toFixed(2) + '°';
}
return value.toFixed(3);
}
function degreesToRadians(degrees) {
return degrees * Math.PI / 180;
}
function radiansToDegrees(radians) {
return radians * 180 / Math.PI;
}
function calculateTriangle() {
clearErrors();
resultDiv.style.display = 'none';
intermediateValuesDiv.innerHTML = ";
missingSideResultSpan.textContent = '–';
missingAngleResultSpan.textContent = '–';
formulaExplanationP.textContent = 'Formula explanation will appear here.';
var a = parseFloat(sideAInput.value);
var b = parseFloat(sideBInput.value);
var c = parseFloat(sideCInput.value);
var alpha = parseFloat(angleAInput.value);
var beta = parseFloat(angleBInput.value);
var gamma = parseFloat(angleCInput.value);
var inputs = { a: a, b: b, c: c, alpha: alpha, beta: beta, gamma: gamma };
var knownSides = 0;
var knownAngles = 0;
var missingSide = null;
var missingAngle = null;
var formula = ";
var intermediate = {};
// Validate inputs
if (isValidNumber(a) && a <= 0) angleAError.textContent = 'Side length must be positive.';
if (isValidNumber(b) && b <= 0) angleBError.textContent = 'Side length must be positive.';
if (isValidNumber(c) && c <= 0) angleCError.textContent = 'Side length must be positive.';
if (isValidNumber(alpha) && (alpha = 180)) angleAError.textContent = 'Angle must be between 0° and 180°.';
if (isValidNumber(beta) && (beta = 180)) angleBError.textContent = 'Angle must be between 0° and 180°.';
if (isValidNumber(gamma) && (gamma = 180)) angleCError.textContent = 'Angle must be between 0° and 180°.';
if (isValidNumber(a)) knownSides++;
if (isValidNumber(b)) knownSides++;
if (isValidNumber(c)) knownSides++;
if (isValidNumber(alpha)) knownAngles++;
if (isValidNumber(beta)) knownAngles++;
if (isValidNumber(gamma)) knownAngles++;
var totalKnown = knownSides + knownAngles;
if (totalKnown c) && (a + c > b) && (b + c > a))) {
formulaExplanationP.textContent = 'Error: The provided side lengths do not form a valid triangle (Triangle Inequality Theorem violated).';
updatePropertiesTable(a, b, c, alpha, beta, gamma);
updateChart(inputs);
return;
}
}
// Check Angle Sum
var angleSum = 0;
if (isValidNumber(alpha)) angleSum += alpha;
if (isValidNumber(beta)) angleSum += beta;
if (isValidNumber(gamma)) angleSum += gamma;
if (knownAngles >= 2 && Math.abs(angleSum – 180) > 1e-6) { // Allow for small floating point errors
formulaExplanationP.textContent = 'Error: The provided angles do not sum to 180 degrees.';
updatePropertiesTable(a, b, c, alpha, beta, gamma);
updateChart(inputs);
return;
}
// — Calculation Logic —
// Case 1: SSS (Find Angles)
if (knownSides === 3 && knownAngles === 0) {
formula = "Law of Cosines (to find angles)";
var cosAlpha = (b*b + c*c – a*a) / (2*b*c);
var cosBeta = (a*a + c*c – b*b) / (2*a*c);
var cosGamma = (a*a + b*b – c*c) / (2*a*b);
if (Math.abs(cosAlpha) <= 1) { alpha = radiansToDegrees(Math.acos(cosAlpha)); } else { alpha = NaN; }
if (Math.abs(cosBeta) <= 1) { beta = radiansToDegrees(Math.acos(cosBeta)); } else { beta = NaN; }
if (Math.abs(cosGamma) = 0) {
c = Math.sqrt(cSquared);
missingSide = c;
intermediate.cSquared = cSquared;
formulaExplanationP.textContent = 'Using the Law of Cosines to find a side when two sides and the included angle are known.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting c² is negative.';
}
}
// Case 3: SAS (Find Side B)
else if (isValidNumber(a) && isValidNumber(c) && isValidNumber(beta) && knownSides === 2 && knownAngles === 1 && isNaN(b)) {
formula = "Law of Cosines (to find side b)";
var bSquared = a*a + c*c – 2*a*c*Math.cos(degreesToRadians(beta));
if (bSquared >= 0) {
b = Math.sqrt(bSquared);
missingSide = b;
intermediate.bSquared = bSquared;
formulaExplanationP.textContent = 'Using the Law of Cosines to find a side when two sides and the included angle are known.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting b² is negative.';
}
}
// Case 4: SAS (Find Side A)
else if (isValidNumber(b) && isValidNumber(c) && isValidNumber(alpha) && knownSides === 2 && knownAngles === 1 && isNaN(a)) {
formula = "Law of Cosines (to find side a)";
var aSquared = b*b + c*c – 2*b*c*Math.cos(degreesToRadians(alpha));
if (aSquared >= 0) {
a = Math.sqrt(aSquared);
missingSide = a;
intermediate.aSquared = aSquared;
formulaExplanationP.textContent = 'Using the Law of Cosines to find a side when two sides and the included angle are known.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting a² is negative.';
}
}
// Case 5: AAS or ASA (Find Side C, then Angle B)
else if (isValidNumber(a) && isValidNumber(alpha) && isValidNumber(beta) && knownSides === 1 && knownAngles === 2 && isNaN(c)) {
formula = "Law of Sines (to find side c)";
gamma = 180 – alpha – beta;
if (gamma > 0) {
c = (a * Math.sin(degreesToRadians(gamma))) / Math.sin(degreesToRadians(alpha));
missingSide = c;
missingAngle = gamma;
intermediate.gamma = gamma;
formulaExplanationP.textContent = 'Using the sum of angles to find angle C, then the Law of Sines to find side c.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting angle C is not positive.';
}
}
// Case 6: AAS or ASA (Find Side B, then Angle C)
else if (isValidNumber(a) && isValidNumber(alpha) && isValidNumber(gamma) && knownSides === 1 && knownAngles === 2 && isNaN(b)) {
formula = "Law of Sines (to find side b)";
beta = 180 – alpha – gamma;
if (beta > 0) {
b = (a * Math.sin(degreesToRadians(beta))) / Math.sin(degreesToRadians(alpha));
missingSide = b;
missingAngle = beta;
intermediate.beta = beta;
formulaExplanationP.textContent = 'Using the sum of angles to find angle B, then the Law of Sines to find side b.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting angle B is not positive.';
}
}
// Case 7: AAS or ASA (Find Side A, then Angle C)
else if (isValidNumber(b) && isValidNumber(beta) && isValidNumber(gamma) && knownSides === 1 && knownAngles === 2 && isNaN(a)) {
formula = "Law of Sines (to find side a)";
alpha = 180 – beta – gamma;
if (alpha > 0) {
a = (b * Math.sin(degreesToRadians(alpha))) / Math.sin(degreesToRadians(beta));
missingSide = a;
missingAngle = alpha;
intermediate.alpha = alpha;
formulaExplanationP.textContent = 'Using the sum of angles to find angle A, then the Law of Sines to find side a.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting angle A is not positive.';
}
}
// Case 8: SSA (Ambiguous Case – Find Angle B, then Side C) – Simplified to one solution
else if (isValidNumber(a) && isValidNumber(b) && isValidNumber(alpha) && knownSides === 2 && knownAngles === 1 && isNaN(c) && isNaN(beta) && isNaN(gamma)) {
formula = "Law of Sines (potential ambiguous case)";
var sinBeta = (b * Math.sin(degreesToRadians(alpha))) / a;
if (sinBeta > 1 || sinBeta 1).';
} else {
beta = radiansToDegrees(Math.asin(sinBeta));
gamma = 180 – alpha – beta;
if (gamma > 0) {
c = (a * Math.sin(degreesToRadians(gamma))) / Math.sin(degreesToRadians(alpha));
missingSide = c;
missingAngle = beta; // Displaying the first calculated angle
intermediate.beta = beta;
intermediate.gamma = gamma;
formulaExplanationP.textContent = 'Using the Law of Sines. Note: SSA can sometimes yield two solutions; this calculates one primary solution.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting angle gamma is not positive.';
}
}
}
// Case 9: SSA (Ambiguous Case – Find Angle C, then Side B) – Simplified to one solution
else if (isValidNumber(a) && isValidNumber(c) && isValidNumber(alpha) && knownSides === 2 && knownAngles === 1 && isNaN(b) && isNaN(beta) && isNaN(gamma)) {
formula = "Law of Sines (potential ambiguous case)";
var sinGamma = (c * Math.sin(degreesToRadians(alpha))) / a;
if (sinGamma > 1 || sinGamma 1).';
} else {
gamma = radiansToDegrees(Math.asin(sinGamma));
beta = 180 – alpha – gamma;
if (beta > 0) {
b = (a * Math.sin(degreesToRadians(beta))) / Math.sin(degreesToRadians(alpha));
missingSide = b;
missingAngle = gamma; // Displaying the first calculated angle
intermediate.gamma = gamma;
intermediate.beta = beta;
formulaExplanationP.textContent = 'Using the Law of Sines. Note: SSA can sometimes yield two solutions; this calculates one primary solution.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting angle beta is not positive.';
}
}
}
// Case 10: SSA (Ambiguous Case – Find Angle A, then Side C) – Simplified to one solution
else if (isValidNumber(b) && isValidNumber(c) && isValidNumber(beta) && knownSides === 2 && knownAngles === 1 && isNaN(a) && isNaN(alpha) && isNaN(gamma)) {
formula = "Law of Sines (potential ambiguous case)";
var sinAlpha = (a * Math.sin(degreesToRadians(beta))) / b; // Oops, 'a' is unknown. Need to use c and beta to find alpha.
// Correct approach: Use Law of Cosines to find 'a' first if SAS, or Law of Sines if AAS/ASA.
// If we have b, c, beta, we need alpha or gamma.
// Let's assume we have b, c, beta and want alpha.
// We can use Law of Cosines to find 'a' IF beta was the included angle. It's not.
// We need to find gamma first using Law of Sines if possible.
// sinGamma / c = sinBeta / b => sinGamma = (c * sinBeta) / b
var sinGamma = (c * Math.sin(degreesToRadians(beta))) / b;
if (sinGamma > 1 || sinGamma 1).';
} else {
gamma = radiansToDegrees(Math.asin(sinGamma));
alpha = 180 – beta – gamma;
if (alpha > 0) {
a = (b * Math.sin(degreesToRadians(alpha))) / Math.sin(degreesToRadians(beta));
missingSide = a;
missingAngle = alpha; // Displaying the first calculated angle
intermediate.alpha = alpha;
intermediate.gamma = gamma;
formulaExplanationP.textContent = 'Using the Law of Sines. Note: SSA can sometimes yield two solutions; this calculates one primary solution.';
} else {
formulaExplanationP.textContent = 'Calculation error: Resulting angle alpha is not positive.';
}
}
}
// Update results display
if (missingSide !== null && !isNaN(missingSide)) {
missingSideResultSpan.textContent = formatValue(missingSide);
resultDiv.style.display = 'block';
}
if (missingAngle !== null && !isNaN(missingAngle)) {
missingAngleResultSpan.textContent = formatValue(missingAngle, true);
resultDiv.style.display = 'block';
}
// Display intermediate values
var intermediateHtml = ";
for (var key in intermediate) {
if (intermediate.hasOwnProperty(key)) {
var label = key.toUpperCase();
if (key === 'alpha' || key === 'beta' || key === 'gamma') {
intermediateHtml += " + label + ': ' + formatValue(intermediate[key], true) + ";
} else {
intermediateHtml += " + label + ': ' + formatValue(intermediate[key]) + ";
}
}
}
if (intermediateHtml) {
intermediateValuesDiv.innerHTML = intermediateHtml;
}
// Update the properties table with potentially updated values
updatePropertiesTable(a, b, c, alpha, beta, gamma);
updateChart(inputs); // Update chart with potentially new values
}
function resetCalculator() {
sideAInput.value = ";
sideBInput.value = ";
sideCInput.value = ";
angleAInput.value = ";
angleBInput.value = ";
angleCInput.value = ";
clearErrors();
resultDiv.style.display = 'none';
intermediateValuesDiv.innerHTML = ";
missingSideResultSpan.textContent = '–';
missingAngleResultSpan.textContent = '–';
formulaExplanationP.textContent = 'Formula explanation will appear here.';
updatePropertiesTable(null, null, null, null, null, null);
updateChart({ a: null, b: null, c: null, alpha: null, beta: null, gamma: null });
}
function copyResults() {
var resultsText = "Triangle Calculation Results:\n\n";
resultsText += "Missing Side: " + missingSideResultSpan.textContent + "\n";
resultsText += "Missing Angle: " + missingAngleResultSpan.textContent + "\n\n";
resultsText += "Intermediate Values:\n";
var intermediateDiv = document.getElementById('intermediateValues');
if (intermediateDiv.innerHTML) {
resultsText += intermediateDiv.textContent.replace(//g, ").replace(//g, '\n');
} else {
resultsText += "None calculated.\n";
}
resultsText += "\n";
resultsText += "Formula Used: " + formulaExplanationP.textContent + "\n\n";
resultsText += "Triangle Properties:\n";
var rows = document.getElementById('propertiesTableBody').getElementsByTagName('tr');
for (var i = 0; i val !== 0)) {
data.datasets.push({
label: 'Calculated Values',
data: calculatedValues,
backgroundColor: [
'rgba(255, 99, 132, 0.2)', // Side A
'rgba(54, 162, 235, 0.2)', // Side B
'rgba(255, 206, 86, 0.2)', // Side C
'rgba(75, 192, 192, 0.2)', // Angle A
'rgba(153, 102, 255, 0.2)', // Angle B
'rgba(255, 159, 64, 0.2)' // Angle C
],
borderColor: [
'rgba(255, 99, 132, 0.5)',
'rgba(54, 162, 235, 0.5)',
'rgba(255, 206, 86, 0.5)',
'rgba(75, 192, 192, 0.5)',
'rgba(153, 102, 255, 0.5)',
'rgba(255, 159, 64, 0.5)'
],
borderWidth: 1
});
}
chartInstance = new Chart(ctx, {
type: 'bar', // Using bar chart for simplicity to show values
data: data,
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
y: {
beginAtZero: true
}
},
plugins: {
title: {
display: true,
text: 'Triangle Side and Angle Values'
}
}
}
});
}
// Initialize chart on load
document.addEventListener('DOMContentLoaded', function() {
var ctx = document.getElementById('triangleChart').getContext('2d');
chartInstance = new Chart(ctx, {
type: 'bar',
data: {
labels: ['Side A', 'Side B', 'Side C', 'Angle A', 'Angle B', 'Angle C'],
datasets: [{
label: 'Initial Values',
data: [0, 0, 0, 0, 0, 0],
backgroundColor: 'rgba(192, 192, 192, 0.6)',
borderColor: 'rgba(192, 192, 192, 1)',
borderWidth: 1
}]
},
options: {
responsive: true,
maintainAspectRatio: false,
scales: { y: { beginAtZero: true } },
plugins: {
title: {
display: true,
text: 'Triangle Side and Angle Values'
}
}
}
});
// Add event listeners for real-time updates
sideAInput.addEventListener('input', calculateTriangle);
sideBInput.addEventListener('input', calculateTriangle);
sideCInput.addEventListener('input', calculateTriangle);
angleAInput.addEventListener('input', calculateTriangle);
angleBInput.addEventListener('input', calculateTriangle);
angleCInput.addEventListener('input', calculateTriangle);
// Initialize properties table
updatePropertiesTable(null, null, null, null, null, null);
});
// FAQ functionality
var faqQuestions = document.querySelectorAll('.faq-question');
faqQuestions.forEach(function(question) {
question.addEventListener('click', function() {
var answer = this.nextElementSibling;
this.classList.toggle('active');
if (answer.style.maxHeight) {
answer.style.maxHeight = null;
} else {
answer.style.maxHeight = answer.scrollHeight + "px";
}
});
});