Solving Triangles Calculator
Accurately determine unknown sides and angles of any triangle.
Triangle Solver
Enter the length of side A (must be positive).
Enter the length of side B (must be positive).
Enter the length of side C (must be positive).
Enter the angle opposite side A (0-180 degrees).
Enter the angle opposite side B (0-180 degrees).
Enter the angle opposite side C (0-180 degrees).
Calculation Results
What is Solving Triangles?
{primary_keyword} is the process of finding the unknown sides and angles of a triangle when some of its properties are known. Triangles are fundamental geometric shapes, and understanding how to solve them is crucial in various fields, including trigonometry, surveying, navigation, engineering, and physics. A triangle is defined by three sides and three angles. If you know at least three of these elements (with at least one side being known), you can typically determine the remaining three elements.
Who should use it?
- Students learning trigonometry and geometry.
- Surveyors measuring land boundaries.
- Navigators determining positions and courses.
- Engineers designing structures and components.
- Physicists analyzing forces and vectors.
- Anyone needing to calculate distances or angles indirectly.
Common Misconceptions:
- All triangles can be solved with just two pieces of information: This is incorrect. For most triangles, you need at least three pieces of information, including at least one side. Special cases like equilateral triangles are exceptions.
- The Law of Sines always gives a unique solution: The Law of Sines can sometimes lead to the "ambiguous case" (SSA), where two different triangles can satisfy the given conditions.
- Angles must always be acute: While many introductory examples use acute angles, triangles can have obtuse angles (greater than 90 degrees).
{primary_keyword} Formula and Mathematical Explanation
The process of {primary_keyword} relies on fundamental trigonometric laws and geometric principles. The primary tools are the Law of Sines, the Law of Cosines, and the properties of triangle angles.
Law of Sines
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and 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).
Formula: a / sin(A) = b / sin(B) = c / sin(C)
Law of Cosines
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It's used when you know all three sides (SSS) or two sides and the included angle (SAS).
Formulas:
a² = b² + c² - 2bc * cos(A)b² = a² + c² - 2ac * cos(B)c² = a² + b² - 2ab * cos(C)
These can be rearranged to solve for angles:
cos(A) = (b² + c² - a²) / 2bccos(B) = (a² + c² - b²) / 2accos(C) = (a² + b² - c²) / 2ab
Angle Sum Property
The sum of the interior angles of any triangle is always 180 degrees.
Formula: A + B + C = 180°
Area Calculation
The area of a triangle can be calculated in several ways, including:
- Using two sides and the included angle:
Area = 0.5 * ab * sin(C) - Using Heron's formula (if all three sides are known):
- Calculate the semi-perimeter, s:
s = (a + b + c) / 2 - Calculate the Area:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
- Calculate the semi-perimeter, s:
Perimeter Calculation
The perimeter is simply the sum of the lengths of the three sides.
Formula: Perimeter = a + b + c
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| a, b, c | Length of sides | Units of length (e.g., meters, feet, cm) | Positive real numbers |
| A, B, C | Measure of angles (opposite sides a, b, c respectively) | Degrees or Radians | (0°, 180°) or (0, π) radians |
| s | Semi-perimeter | Units of length | Positive real number |
| Area | Area enclosed by the triangle | Square units (e.g., m², ft²) | Positive real number |
| Perimeter | Sum of side lengths | Units of length | Positive real number |
Practical Examples (Real-World Use Cases)
Example 1: Surveying a Plot of Land (SAS Case)
A surveyor needs to determine the dimensions of a triangular plot of land. They measure two sides and the angle between them. Side A is 100 meters, Side B is 120 meters, and the included Angle C is 75 degrees.
Inputs:
- Side A = 100 m
- Side B = 120 m
- Angle C = 75°
Calculations:
- Using the Law of Cosines to find Side C:
C² = 100² + 120² - 2 * 100 * 120 * cos(75°)C² = 10000 + 14400 - 24000 * 0.2588C² = 24400 - 6211.2C² = 18188.8C = sqrt(18188.8) ≈ 134.87 m - Using the Law of Sines to find Angle A:
sin(A) / a = sin(C) / csin(A) / 100 = sin(75°) / 134.87sin(A) = (100 * sin(75°)) / 134.87sin(A) = (100 * 0.9659) / 134.87 ≈ 0.7161A = arcsin(0.7161) ≈ 45.73° - Finding Angle B using the Angle Sum Property:
B = 180° - C - AB = 180° - 75° - 45.73° ≈ 59.27° - Area = 0.5 * a * b * sin(C) = 0.5 * 100 * 120 * sin(75°) ≈ 5800 m²
- Perimeter = a + b + c = 100 + 120 + 134.87 ≈ 354.87 m
Interpretation: The surveyor now knows all sides (100m, 120m, 134.87m) and angles (45.73°, 59.27°, 75°) of the plot, allowing for accurate mapping and boundary definition.
Example 2: Navigation (AAS Case)
A ship is sailing. At point P, the captain observes a lighthouse L at a bearing of 045°. The ship travels 5 km due East to point Q. At point Q, the lighthouse L is observed at a bearing of 330°.
Inputs:
- Side PQ = 5 km
- Angle at P (relative to East): The bearing is 045°, so the angle inside the triangle formed by PQ and PL is 180° – 45° = 135° (Angle P).
- Angle at Q (relative to East): The bearing is 330°, which is 30° West of North. The angle inside the triangle formed by QP (Westward direction) and QL is 90° + 30° = 120° (Angle Q).
- Wait, this is not AAS. Let's re-evaluate. The angles relative to North are 45° and 330°. The angle between the North line at P and the line PL is 45°. The angle between the North line at Q and the line QL is 30° (360-330). Since the North lines at P and Q are parallel, the alternate interior angle between the Eastward line PQ and the line QL is 30°. So, Angle Q = 30°. The angle between the Eastward line PQ and the line PL is 45°. So, Angle P = 45°.
- Side PQ = 5 km
- Angle P = 45°
- Angle Q = 30°
Calculations:
- Find Angle L using the Angle Sum Property:
L = 180° - P - QL = 180° - 45° - 30° = 105° - Use the Law of Sines to find Side PL (let's call it q):
q / sin(Q) = PQ / sin(L)q / sin(30°) = 5 / sin(105°)q = (5 * sin(30°)) / sin(105°)q = (5 * 0.5) / 0.9659 ≈ 2.588 km - Use the Law of Sines to find Side QL (let's call it p):
p / sin(P) = PQ / sin(L)p / sin(45°) = 5 / sin(105°)p = (5 * sin(45°)) / sin(105°)p = (5 * 0.7071) / 0.9659 ≈ 3.660 km - Area = 0.5 * p * q * sin(L) = 0.5 * 3.660 * 2.588 * sin(105°) ≈ 4.54 km²
- Perimeter = PQ + q + p = 5 + 2.588 + 3.660 ≈ 11.248 km
Interpretation: The ship knows its distance to the lighthouse from its current position (PL ≈ 2.59 km) and its distance to the lighthouse from the next position (QL ≈ 3.66 km), which is vital for navigation and avoiding hazards.
How to Use This Solving Triangles Calculator
Our {primary_keyword} calculator is designed for ease of use. Follow these steps:
- Identify Knowns: Determine which sides and angles of your triangle you know. You need at least three pieces of information, including at least one side length.
- Input Values: Enter the known values into the corresponding fields. Use positive numbers for lengths and values between 0 and 180 degrees for angles.
- Select Calculation Mode (Implicit): The calculator intelligently determines the type of triangle problem (SSS, SAS, ASA, AAS, SSA) based on the inputs provided. If you provide conflicting information (e.g., sides that violate the triangle inequality, or angles that don't sum to 180°), it will indicate an error.
- Click Calculate: Press the "Calculate" button.
- Review Results: The calculator will display the primary results (e.g., a missing side or angle), intermediate values (other calculated sides/angles, area, perimeter), and the formulas used.
- Interpret: Use the results for your specific application, whether it's construction, navigation, or academic study.
How to Read Results:
- The Main Result highlights a key unknown value.
- Intermediate Results provide all other calculated sides, angles, the area, and the perimeter.
- The Formula Explanation briefly describes the trigonometric laws or geometric principles applied.
- The Table summarizes all known and calculated values for clarity.
- The Chart visually represents the triangle's proportions (if possible with the given data).
Decision-Making Guidance: Use the calculated values to verify measurements, plan routes, design structures, or solve complex geometric problems. Ensure the results are consistent with the triangle inequality theorem (the sum of any two sides must be greater than the third side) and that angles sum to 180°.
Key Factors That Affect {primary_keyword} Results
While the mathematical principles are fixed, several factors influence the accuracy and applicability of {primary_keyword}:
- Accuracy of Input Measurements: The most significant factor. Small errors in measuring sides or angles can lead to larger discrepancies in calculated values, especially in large or complex triangles. This is critical in surveying and engineering.
- Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle 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 valid triangle can be formed.
- Ambiguous Case (SSA): When given two sides and a non-included angle (SSA), there might be zero, one, or two possible triangles. Our calculator aims to identify this, but careful interpretation is needed. The calculator will typically prioritize the solution based on standard trigonometric functions.
- Units Consistency: Ensure all side lengths are in the same unit (e.g., all meters, all feet). Angles must be consistently in degrees or radians as required by the calculation context (our calculator uses degrees).
- Rounding Errors: Intermediate calculations involving trigonometric functions can introduce small rounding errors. Using sufficient precision in calculations helps mitigate this.
- Degenerate Triangles: Cases where angles approach 0° or 180°, or where sides sum exactly (a + b = c), result in a "flat" triangle with zero area. The calculator might handle these as edge cases or indicate impossibility.
- Precision of Tools: The precision of the measuring instruments used in real-world scenarios (e.g., theodolites, laser measures) directly impacts the reliability of the input data.
- Contextual Constraints: In practical applications like engineering or physics, physical constraints (e.g., material strength, maximum allowable angles) might limit the possible solutions even if mathematically valid.
Frequently Asked Questions (FAQ)
What information do I need to solve a triangle?
You need at least three pieces of information, including at least one side length. Common combinations include Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), Side-Side-Side (SSS), and Side-Side-Angle (SSA).
Can I solve a triangle if I only know the three angles?
No. Knowing only the three angles (AAA) defines the shape but not the size of the triangle. Infinitely many similar triangles can have the same three angles. You need at least one side length to determine the scale.
What is the ambiguous case (SSA)?
The ambiguous case occurs when you are given two sides and an angle opposite one of them (SSA). Depending on the lengths and the angle, there might be zero, one, or two possible triangles that fit the given information. Our calculator attempts to handle this, but visual inspection or further context might be needed.
How do I ensure my side lengths form a valid triangle?
The Triangle Inequality Theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. For example, if sides are a, b, and c, then a + b > c, a + c > b, and b + c > a must all be true.
Does the calculator handle right-angled triangles specifically?
Yes, the general laws (Law of Sines, Law of Cosines) work for all triangles, including right-angled ones. For right triangles, you can also use basic trigonometric ratios (SOH CAH TOA) and the Pythagorean theorem (a² + b² = c²), which are special cases of the general laws.
What if I input conflicting information?
The calculator will display error messages indicating invalid input, such as side lengths violating the triangle inequality or angle sums not equaling 180 degrees.
Can I use this calculator for triangles in 3D space?
This calculator is designed for solving triangles in a 2D plane. Solving triangles in 3D space requires more advanced vector mathematics or spherical trigonometry.
How accurate are the results?
The accuracy depends on the precision of your input values and the limitations of floating-point arithmetic in the calculation. For most practical purposes, the results are highly accurate. Always double-check critical measurements.
Related Tools and Internal Resources
Angle " + (sideOppositeSide2 === inputs.A ? 'A' : (sideOppositeSide2 === inputs.B ? 'B' : 'C')) + ": " + angle2_1.toFixed(3) + "°
";
intermediateHTML += "Angle " + (sideOppositeAngle1 === inputs.A ? 'A' : (sideOppositeAngle1 === inputs.B ? 'B' : 'C')) + ": " + angle3_1.toFixed(3) + "°
";
var finalA = sideOppositeAngle1 === inputs.A ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.A ? angle2_1 : angle3_1);
var finalB = sideOppositeAngle1 === inputs.B ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.B ? angle2_1 : angle3_1);
var finalC = sideOppositeAngle1 === inputs.C ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.C ? angle2_1 : angle3_1);
var finala = sideOppositeAngle1 === inputs.a ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.a ? angle2_1 : angle3_1);
var finalb = sideOppositeAngle1 === inputs.b ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.b ? angle2_1 : angle3_1);
var finalc = sideOppositeAngle1 === inputs.c ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.c ? angle2_1 : angle3_1);
if (sideOppositeSide2 === inputs.A) { finalA = angle2_1; finalB = angle3_1; }
else if (sideOppositeSide2 === inputs.B) { finalB = angle2_1; finalA = angle3_1; }
else { finalC = angle2_1; finalA = angle3_1; } // Assuming sideOppositeSide2 is C
if (side1 === inputs.a) { finala = side1; } else if (side1 === inputs.b) { finalb = side1; } else { finalc = side1; }
if (side2 === inputs.a) { finala = side2; } else if (side2 === inputs.b) { finalb = side2; } else { finalc = side2; }
if (side3_1 === inputs.a) { finala = side3_1; } else if (side3_1 === inputs.b) { finalb = side3_1; } else { finalc = side3_1; }
results.A = finalA; results.B = finalB; results.C = finalC;
results.a = finala; results.b = finalb; results.c = finalc;
results.area = 0.5 * finala * finalb * Math.sin(degreesToRadians(finalC));
results.perimeter = finala + finalb + finalc;
}
if (validSolution2) {
if (validSolution1) intermediateHTML += ""; intermediateHTML += "
Angle " + (sideOppositeSide2 === inputs.A ? 'A' : (sideOppositeSide2 === inputs.B ? 'B' : 'C')) + ": " + angle2_2.toFixed(3) + "°
";
intermediateHTML += "Angle " + (sideOppositeAngle1 === inputs.A ? 'A' : (sideOppositeAngle1 === inputs.B ? 'B' : 'C')) + ": " + angle3_2.toFixed(3) + "°
";
var finalA2 = sideOppositeAngle1 === inputs.A ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.A ? angle2_2 : angle3_2);
var finalB2 = sideOppositeAngle1 === inputs.B ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.B ? angle2_2 : angle3_2);
var finalC2 = sideOppositeAngle1 === inputs.C ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.C ? angle2_2 : angle3_2);
var finala2 = sideOppositeAngle1 === inputs.a ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.a ? angle2_2 : angle3_2);
var finalb2 = sideOppositeAngle1 === inputs.b ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.b ? angle2_2 : angle3_2);
var finalc2 = sideOppositeAngle1 === inputs.c ? sideOppositeAngle1 : (sideOppositeSide2 === inputs.c ? angle2_2 : angle3_2);
if (sideOppositeSide2 === inputs.A) { finalA2 = angle2_2; finalB2 = angle3_2; }
else if (sideOppositeSide2 === inputs.B) { finalB2 = angle2_2; finalA2 = angle3_2; }
else { finalC2 = angle2_2; finalA2 = angle3_2; }
if (side1 === inputs.a) { finala2 = side1; } else if (side1 === inputs.b) { finalb2 = side1; } else { finalc2 = side1; }
if (side2 === inputs.a) { finala2 = side2; } else if (side2 === inputs.b) { finalb2 = side2; } else { finalc2 = side2; }
if (side3_2 === inputs.a) { finala2 = side3_2; } else if (side3_2 === inputs.b) { finalb2 = side3_2; } else { finalc2 = side3_2; }
if (validSolution1) {
displayResult += "Solution 2: Side " + (sideOppositeSide2 === inputs.A ? 'A' : (sideOppositeSide2 === inputs.B ? 'B' : 'C')) + " = " + side3_2.toFixed(3);
} else {
displayResult = "Solution 1: Side " + (sideOppositeSide2 === inputs.A ? 'A' : (sideOppositeSide2 === inputs.B ? 'B' : 'C')) + " = " + side3_2.toFixed(3);
}
results.A = finalA2; results.B = finalB2; results.C = finalC2;
results.a = finala2; results.b = finalb2; results.c = finalc2;
results.area = 0.5 * finala2 * finalb2 * Math.sin(degreesToRadians(finalC2));
results.perimeter = finala2 + finalb2 + finalc2;
}
if (!validSolution1 && !validSolution2) {
getElement("mainResult").textContent = "No Solution";
getElement("resultUnit").textContent = "Sides/angle combination invalid.";
getElement("intermediateResults").innerHTML = "";
getElement("formulaExplanation").textContent = formula;
updateChart([], []);
return;
}
getElement("mainResult").textContent = displayResult;
getElement("resultUnit").textContent = "";
getElement("intermediateResults").innerHTML = intermediateHTML;
getElement("formulaExplanation").textContent = formula;
// Prepare table data
tableData.push({ label: "Knowns", values: {} });
tableData.push({ label: "Calculated", values: {} });
var knowns = { a: inputs.a, b: inputs.b, c: inputs.c, A: inputs.A, B: inputs.B, C: inputs.C };
var calculated = { a: results.a, b: results.b, c: results.c, A: results.A, B: results.B, C: results.C };
var keys = ['a', 'b', 'c', 'A', 'B', 'C'];
keys.forEach(function(key) {
if (knowns[key] !== null) tableData[0].values[key] = knowns[key];
if (calculated[key] !== null && knowns[key] === null) tableData[1].values[key] = calculated[key];
});
generateTable(tableData, results.area, results.perimeter);
updateChart(results, inputs);
return; // Exit after SSA handling
}
}
// If calculation is possible, display results
if (calculationPossible) {
var mainResultText = "";
var resultUnitText = "";
var intermediateHTML = "";
var tableData = [];
var finalA = results.A !== null ? results.A : inputs.A;
var finalB = results.B !== null ? results.B : inputs.B;
var finalC = results.C !== null ? results.C : inputs.C;
var finala = results.a !== null ? results.a : inputs.a;
var finalb = results.b !== null ? results.b : inputs.b;
var finalc = results.c !== null ? results.c : inputs.c;
// Determine the primary result to highlight
if (finala === null) { mainResultText = "Side A = " + finala.toFixed(3); resultUnitText = ""; }
else if (finalb === null) { mainResultText = "Side B = " + finalb.toFixed(3); resultUnitText = ""; }
else if (finalc === null) { mainResultText = "Side C = " + finalc.toFixed(3); resultUnitText = ""; }
else if (finalA === null) { mainResultText = "Angle A = " + finalA.toFixed(3) + "°"; resultUnitText = ""; }
else if (finalB === null) { mainResultText = "Angle B = " + finalB.toFixed(3) + "°"; resultUnitText = ""; }
else if (finalC === null) { mainResultText = "Angle C = " + finalC.toFixed(3) + "°"; resultUnitText = ""; }
else { mainResultText = "All values solved"; resultUnitText = ""; }
getElement("mainResult").textContent = mainResultText;
getElement("resultUnit").textContent = resultUnitText;
// Populate intermediate results
if (finala !== null && inputs.a === null) intermediateHTML += "Side A: " + finala.toFixed(3) + "
";
if (finalb !== null && inputs.b === null) intermediateHTML += "Side B: " + finalb.toFixed(3) + "
";
if (finalc !== null && inputs.c === null) intermediateHTML += "Side C: " + finalc.toFixed(3) + "
";
if (finalA !== null && inputs.A === null) intermediateHTML += "Angle A: " + finalA.toFixed(3) + "°
";
if (finalB !== null && inputs.B === null) intermediateHTML += "Angle B: " + finalB.toFixed(3) + "°
";
if (finalC !== null && inputs.C === null) intermediateHTML += "Angle C: " + finalC.toFixed(3) + "°
";
if (results.area !== null) intermediateHTML += "Area: " + results.area.toFixed(3) + "
";
if (results.perimeter !== null) intermediateHTML += "Perimeter: " + results.perimeter.toFixed(3) + "
";
getElement("intermediateResults").innerHTML = intermediateHTML;
getElement("formulaExplanation").textContent = formula;
// Prepare table data
tableData.push({ label: "Known Values", values: {} });
tableData.push({ label: "Calculated Values", values: {} });
var knowns = { a: inputs.a, b: inputs.b, c: inputs.c, A: inputs.A, B: inputs.B, C: inputs.C };
var calculated = { a: finala, b: finalb, c: finalc, A: finalA, B: finalB, C: finalC };
var keys = ['a', 'b', 'c', 'A', 'B', 'C'];
keys.forEach(function(key) {
if (knowns[key] !== null) tableData[0].values[key] = knowns[key];
if (calculated[key] !== null && knowns[key] === null) tableData[1].values[key] = calculated[key];
});
generateTable(tableData, results.area, results.perimeter);
updateChart(results, inputs);
getElement("mainResultContainer").style.display = "block";
} else {
getElement("mainResult").textContent = "Enter at least 3 values (including one side)";
getElement("resultUnit").textContent = "";
getElement("intermediateResults").innerHTML = "";
getElement("formulaExplanation").textContent = "";
getElement("tableContainer").innerHTML = "";
updateChart([], []);
getElement("mainResultContainer").style.display = "none";
}
}
function generateTable(data, area, perimeter) {
var tableContainer = getElement("tableContainer");
var tableHTML = "| Property | Value | Unit |
|---|---|---|
| " + section.label + " | ||
| " + key.toUpperCase() + " | "; tableHTML += "" + (typeof value === 'number' ? value.toFixed(3) : value) + " | "; tableHTML += "" + (unitMap[key] || "") + " | "; tableHTML += "
| Area | " + area.toFixed(3) + " | sq. units |
| Perimeter | " + perimeter.toFixed(3) + " | units |
/g, '- ').replace(//g, '\n').trim() + "\n";
}
if (formula) {
textToCopy += "\nFormula Used: " + formula + "\n";
}
if (table) {
textToCopy += "\nTable Summary:\n" + table + "\n";
}
// Use a temporary textarea to copy
var tempTextArea = document.createElement("textarea");
tempTextArea.value = textToCopy;
document.body.appendChild(tempTextArea);
tempTextArea.select();
try {
document.execCommand("copy");
alert("Results copied to clipboard!");
} catch (err) {
alert("Failed to copy results. Please copy manually.");
}
document.body.removeChild(tempTextArea);
}
function resetCalculator() {
getElement("sideA").value = "";
getElement("sideB").value = "";
getElement("sideC").value = "";
getElement("angleA").value = "";
getElement("angleB").value = "";
getElement("angleC").value = "";
clearErrorMessages();
getElement("mainResult").textContent = "Enter values to calculate";
getElement("resultUnit").textContent = "";
getElement("intermediateResults").innerHTML = "";
getElement("formulaExplanation").textContent = "";
getElement("tableContainer").innerHTML = "";
getElement("mainResultContainer").style.display = "none";
var canvas = getElement('triangleChart');
var ctx = canvas.getContext('2d');
ctx.clearRect(0, 0, canvas.width, canvas.height);
getElement('chartLegend').innerHTML = ";
}
// Add event listeners for real-time updates
var inputs = document.querySelectorAll('.loan-calc-container input');
inputs.forEach(function(input) {
input.addEventListener('input', function() {
// Only calculate if there are enough inputs to potentially solve
var currentInputs = {
a: getElement("sideA").value,
b: getElement("sideB").value,
c: getElement("sideC").value,
A: getElement("angleA").value,
B: getElement("angleB").value,
C: getElement("angleC").value
};
var filledCount = 0;
for (var key in currentInputs) {
if (currentInputs[key] !== "") {
filledCount++;
}
}
if (filledCount >= 3) {
calculateTriangle();
} else {
// Clear results if not enough inputs
getElement("mainResult").textContent = "Enter at least 3 values (including one side)";
getElement("resultUnit").textContent = "";
getElement("intermediateResults").innerHTML = "";
getElement("formulaExplanation").textContent = "";
getElement("tableContainer").innerHTML = "";
getElement("mainResultContainer").style.display = "none";
var canvas = getElement('triangleChart');
var ctx = canvas.getContext('2d');
ctx.clearRect(0, 0, canvas.width, canvas.height);
getElement('chartLegend').innerHTML = ";
}
});
});
// FAQ toggles
var faqQuestions = document.querySelectorAll('.faq-question');
faqQuestions.forEach(function(question) {
question.addEventListener('click', function() {
var faqItem = this.parentElement;
faqItem.classList.toggle('open');
});
});
// Initial calculation on load if defaults are set (optional)
// calculateTriangle();