Calculate unknown sides and angles of a right-angled triangle using basic trigonometric functions (sine, cosine, tangent).
Enter the length of the side adjacent to angle B (and opposite angle C, the right angle).
Enter the length of the side opposite angle B (and adjacent to angle A).
Enter the length of the hypotenuse. If Side A and Side B are entered, this will be calculated.
Enter the angle A (in degrees). If Side A and Side B are entered, this will be calculated.
Enter the angle B (in degrees). If Side A and Side B are entered, this will be calculated.
Calculation Results
Hypotenuse:
Angle A: degrees
Angle B: degrees
Area:
Side A
Side B
Angle C
90 degrees
Formulas used: Pythagorean theorem ($c^2 = a^2 + b^2$), tan(B) = b/a, sin(B) = b/c, cos(B) = a/c, A + B = 90°. Area = 0.5 * base * height.
Side and Angle Relationships
Visualizing the relationship between sides and angles.
Trigonometric Ratios
Ratio
Formula
Value (for Angle B)
Sine (sin B)
Opposite / Hypotenuse
Cosine (cos B)
Adjacent / Hypotenuse
Tangent (tan B)
Opposite / Adjacent
An indispensable tool for students, engineers, and anyone working with geometric shapes, the trig calculator right angle simplifies complex calculations involving right-angled triangles. Understanding how to calculate unknown sides and angles is fundamental in many scientific and practical fields. This tool empowers you to quickly find these values without manual computation.
What is a Right Triangle Trigonometry Calculator?
A trig calculator right angle is a specialized online tool designed to compute the missing sides and angles of a triangle that contains one 90-degree angle. By inputting known values—such as the lengths of two sides, or one side and one acute angle—the calculator utilizes the principles of trigonometry (specifically sine, cosine, and tangent) and the Pythagorean theorem to derive the unknown measurements. It's an essential instrument for anyone needing to work with right-angled triangles, from high school students learning geometry to professionals in fields like construction, navigation, and physics.
Who should use it?
Students: Learning trigonometry and geometry concepts.
Engineers: Calculating forces, structures, and measurements.
Architects: Designing buildings and structures.
Surveyors: Measuring land and distances.
Navigators: Determining positions and courses.
DIY Enthusiasts: For projects requiring precise angles and lengths.
Common misconceptions about right triangle calculations include:
Assuming all triangles can be solved with basic trig ratios; these apply specifically to right-angled triangles.
Confusing which side is opposite or adjacent relative to a given angle.
Forgetting to convert degrees to radians (or vice versa) if a calculator or function requires it (though this tool works directly with degrees).
Overlooking the fact that the sum of the two acute angles in a right triangle is always 90 degrees.
Right Triangle Trigonometry Formula and Mathematical Explanation
The foundation of the trig calculator right angle lies in a few core mathematical principles:
1. The Pythagorean Theorem
For any right-angled triangle with sides labelled 'a' and 'b' (the legs) and hypotenuse 'c' (the side opposite the right angle), the theorem states:
$a^2 + b^2 = c^2$
This allows us to find the length of any one side if the other two are known.
2. Trigonometric Ratios (SOH CAH TOA)
These ratios relate the angles of a right triangle to the lengths of its sides. Let's consider angle B:
Sine (sin): The ratio of the length of the side opposite angle B to the length of the hypotenuse.
By using the inverse trigonometric functions (arcsin, arccos, arctan), we can find the angle B if we know the ratio of the sides.
3. Angle Sum Property
In any triangle, the sum of all interior angles is 180 degrees. In a right triangle, one angle is 90 degrees, so the sum of the other two acute angles (A and B) must be 90 degrees:
$A + B = 90^\circ$
4. Area of a Right Triangle
The area is half the product of the two legs (the sides forming the right angle):
Area = $\frac{1}{2} \times a \times b$
Variables Table
Variable Definitions for Right Triangles
Variable
Meaning
Unit
Typical Range
Side A (a)
Length of the leg adjacent to angle B
Length Units (e.g., meters, feet)
> 0
Side B (b)
Length of the leg opposite angle B
Length Units (e.g., meters, feet)
> 0
Hypotenuse (c)
Length of the side opposite the right angle (longest side)
Length Units (e.g., meters, feet)
> Side A and Side B
Angle A (A)
Acute angle opposite Side B
Degrees or Radians
(0, 90) degrees
Angle B (B)
Acute angle opposite Side A
Degrees or Radians
(0, 90) degrees
Angle C (C)
The right angle
Degrees
90 degrees
Area
The space enclosed by the triangle
Square Units (e.g., m², ft²)
> 0
Practical Examples (Real-World Use Cases)
Let's explore how the trig calculator right angle can be applied:
Example 1: Ladder Against a Wall
Scenario: You have a 10-foot ladder leaning against a wall. The base of the ladder is 3 feet away from the wall. How high up the wall does the ladder reach, and what angle does it make with the ground?
Inputs:
Hypotenuse = 10 feet
Side A (distance from wall) = 3 feet
Using the Calculator:
1. Enter Hypotenuse = 10 and Side A = 3.
2. The calculator computes Side B (height on the wall) using the Pythagorean theorem: $b = \sqrt{c^2 – a^2} = \sqrt{10^2 – 3^2} = \sqrt{100 – 9} = \sqrt{91} \approx 9.54$ feet.
3. It then calculates Angle B (angle with the ground) using cosine: $\cos(B) = \frac{a}{c} = \frac{3}{10} = 0.3$. So, $B = \arccos(0.3) \approx 72.54$ degrees.
4. Angle A is $90 – B \approx 90 – 72.54 = 17.46$ degrees.
Interpretation: The ladder reaches approximately 9.54 feet up the wall and makes an angle of about 72.54 degrees with the ground. This information is crucial for ensuring ladder stability and safety.
Example 2: Determining the Height of a Building
Scenario: You are standing 50 meters away from the base of a building. You measure the angle from your eye level to the top of the building to be 40 degrees. Assuming your eye level is 1.5 meters above the ground, what is the total height of the building?
Inputs:
Side A (distance from building) = 50 meters
Angle B (angle of elevation) = 40 degrees
(We'll calculate the height from eye level upwards, then add eye level height)
Using the Calculator:
1. Set Angle B = 40 degrees and Side A (adjacent) = 50 meters.
2. The calculator computes Side B (height from eye level to top) using tangent: $\tan(B) = \frac{b}{a} \implies b = a \times \tan(B) = 50 \times \tan(40^\circ)$. $\tan(40^\circ) \approx 0.839$. So, $b \approx 50 \times 0.839 = 41.95$ meters.
3. The total height of the building is Side B + eye level height $\approx 41.95 + 1.5 = 43.45$ meters.
Interpretation: The building is approximately 43.45 meters tall. This application of the trig calculator right angle is common in surveying and architecture.
How to Use This Right Triangle Trigonometry Calculator
Our trig calculator right angle is designed for ease of use. Follow these simple steps:
Identify Knowns: Determine which sides and/or angles of your right-angled triangle are already known. Remember, angle C is always 90 degrees.
Input Values: Enter the known values into the corresponding fields (Side A, Side B, Hypotenuse, Angle A, Angle B). You generally only need two pieces of information (excluding the 90-degree angle) to solve for the rest. For instance, entering two sides will calculate the hypotenuse and both acute angles. Entering one side and one acute angle will calculate the other side and the other acute angle.
Automatic Calculation: As you input valid numbers, the calculator updates the results in real-time. If you input only Side A and Side B, it will calculate the Hypotenuse and the angles. If you input a side and an angle, it will calculate the remaining side and angle.
Review Results: The primary results (Hypotenuse, Angles A & B, Area) will be displayed prominently. Intermediate values and trigonometric ratios are also shown in tables for clarity.
Use 'Copy Results': If you need to record or share the calculated values, click the 'Copy Results' button. This will copy all key outputs and assumptions to your clipboard.
Reset: If you need to start over or clear the inputs, click the 'Reset' button to return the calculator to its default state.
Decision-Making Guidance:
Use the calculated sides to determine material quantities or structural integrity.
Use the calculated angles to ensure proper alignment, slope, or direction.
The area calculation can be useful for estimating surface coverage or material needs.
This trig calculator right angle is a versatile tool that can support a wide range of geometric problem-solving tasks.
Key Factors That Affect Right Triangle Calculations
While the core formulas for a trig calculator right angle are fixed, several factors can influence how you interpret or apply the results in real-world scenarios:
Measurement Accuracy: In practical applications (like surveying or construction), the precision of your initial measurements directly impacts the accuracy of the calculated values. Small errors in input lengths or angles can lead to larger discrepancies in the results, especially for complex constructions.
Units of Measurement: Consistently using the same units (e.g., all in meters, or all in feet) for side lengths is crucial. Ensure your angle inputs are in degrees if the calculator expects degrees, as mixing units can lead to significant errors.
Assumptions about 'Right Angle': This calculator is exclusively for right-angled triangles. If the angle you assume to be 90 degrees is slightly off, the calculations will be inaccurate. For non-right triangles, different trigonometric laws (like the Law of Sines or Cosines) are required.
Contextual Constraints: Real-world applications often have physical limitations. For example, a ladder cannot lean at an angle too acute (close to 0 degrees) or too obtuse (close to 90 degrees) without compromising safety, even if the math allows for it.
Level of Precision Required: Depending on the application, you might need to round results to a certain number of decimal places. Engineering or high-precision manufacturing demands greater accuracy than a simple DIY project.
Data Input Errors: Simple typos or entering values in the wrong fields are common pitfalls. Always double-check your inputs before relying on the calculated outputs. The validation messages help prevent invalid entries like negative lengths.
External Factors (Indirect Impact): While not directly part of the trig calculation itself, factors like material stress, environmental conditions (temperature affecting expansion), or ground unevenness (for building foundations) are critical considerations when translating calculated lengths and angles into physical structures.
Frequently Asked Questions (FAQ)
What's the difference between Angle A and Angle B?
Angle A is opposite Side B, and Angle B is opposite Side A. In a right triangle, both A and B are acute angles (less than 90 degrees), and their sum is always 90 degrees.
Can I use this calculator for non-right triangles?
No, this specific calculator is designed exclusively for right-angled triangles. For oblique (non-right) triangles, you would need to use the Law of Sines or the Law of Cosines.
What if I enter the hypotenuse and one leg?
The calculator will use the Pythagorean theorem ($a^2 + b^2 = c^2$) to find the missing leg and then use trigonometric ratios to find the angles.
What if I enter one leg and one angle (not the right angle)?
The calculator will use the trigonometric ratios (SOH CAH TOA) to find the other leg and the hypotenuse, and then determine the remaining acute angle using $A + B = 90^\circ$.
Why is the area calculation important?
The area calculation is useful in various applications, such as determining the amount of paint needed for a triangular section of a wall, calculating the surface area of a triangular piece of land, or finding the capacity of a triangular container.
What does 'SOH CAH TOA' mean?
'SOH CAH TOA' is a mnemonic device to remember the basic trigonometric ratios: Sine = Opposite/Hypotenuse (SOH), Cosine = Adjacent/Hypotenuse (CAH), Tangent = Opposite/Adjacent (TOA).
How accurate are the results?
The accuracy depends on the precision of the input values and the internal floating-point calculations of the computer. For most practical purposes, the results are highly accurate. Always double-check critical measurements.
Can I calculate trigonometric values for angles greater than 90 degrees?
This calculator is specifically for right-angled triangles, meaning it deals with angles between 0 and 90 degrees. Trigonometric functions can be defined for all angles, but this tool focuses on the geometric interpretation within a right triangle.
var chartInstance = null; // Global variable to hold the chart instance
function getElement(id) {
return document.getElementById(id);
}
function setDisplay(id, style) {
getElement(id).style.display = style;
}
function validateInput(value, id, errorId, min, max) {
var errorElement = getElement(errorId);
if (value === "") {
errorElement.textContent = "This field cannot be empty.";
errorElement.style.display = "block";
return false;
}
var numValue = parseFloat(value);
if (isNaN(numValue)) {
errorElement.textContent = "Please enter a valid number.";
errorElement.style.display = "block";
return false;
}
if (numValue = max) {
errorElement.textContent = "Value must be less than " + max + ".";
errorElement.style.display = "block";
return false;
}
errorElement.style.display = "none";
return true;
}
function degreesToRadians(degrees) {
return degrees * Math.PI / 180;
}
function radiansToDegrees(radians) {
return radians * 180 / Math.PI;
}
function calculateTrig() {
var sideAInput = getElement("sideA");
var sideBInput = getElement("sideB");
var hypotenuseInput = getElement("hypotenuse");
var angleAInput = getElement("angleA");
var angleBInput = getElement("angleB");
var sideA = parseFloat(sideAInput.value);
var sideB = parseFloat(sideBInput.value);
var hypotenuse = parseFloat(hypotenuseInput.value);
var angleA = parseFloat(angleAInput.value);
var angleB = parseFloat(angleBInput.value);
var isValid = true;
var inputsUsed = 0;
// Validate inputs that are provided
if (sideAInput.value !== "") {
isValid = isValid && validateInput(sideAInput.value, "sideA", "sideAError", 0);
if (isValid) inputsUsed++;
}
if (sideBInput.value !== "") {
isValid = isValid && validateInput(sideBInput.value, "sideB", "sideBError", 0);
if (isValid) inputsUsed++;
}
if (hypotenuseInput.value !== "") {
isValid = isValid && validateInput(hypotenuseInput.value, "hypotenuse", "hypotenuseError", 0);
if (isValid) inputsUsed++;
}
if (angleAInput.value !== "") {
isValid = isValid && validateInput(angleAInput.value, "angleA", "angleAError", 0, 90);
if (isValid) inputsUsed++;
}
if (angleBInput.value !== "") {
isValid = isValid && validateInput(angleBInput.value, "angleB", "angleBError", 0, 90);
if (isValid) inputsUsed++;
}
// Basic check: we need at least two valid pieces of info (excluding the 90 degree angle)
if (inputsUsed < 2) {
setDisplay("result", "none");
setDisplay("intermediateResults", "none");
setDisplay("copyBtn", "none");
if (isValid) { // If inputs are valid but not enough
document.getElementById("result").innerHTML = "
Please enter at least two known values.
";
setDisplay("result", "block");
}
return;
}
var calculatedSideA = sideA;
var calculatedSideB = sideB;
var calculatedHypotenuse = hypotenuse;
var calculatedAngleA = angleA;
var calculatedAngleB = angleB;
// — Calculation Logic —
// Prioritize calculations based on common inputs
// Case 1: Side A and Side B provided
if (inputsUsed === 2 && sideA !== undefined && sideB !== undefined && sideA > 0 && sideB > 0) {
calculatedHypotenuse = Math.sqrt(Math.pow(sideA, 2) + Math.pow(sideB, 2));
calculatedAngleB = radiansToDegrees(Math.atan(sideB / sideA));
calculatedAngleA = 90 – calculatedAngleB;
}
// Case 2: Side A and Angle B provided
else if (inputsUsed >= 2 && sideA !== undefined && sideA > 0 && angleB !== undefined && angleB > 0 && angleB = 2 && sideB !== undefined && sideB > 0 && angleB !== undefined && angleB > 0 && angleB = 2 && hypotenuse !== undefined && hypotenuse > 0 && angleB !== undefined && angleB > 0 && angleB = 2 && hypotenuse !== undefined && hypotenuse > 0 && sideA !== undefined && sideA > 0 && sideA = 2 && hypotenuse !== undefined && hypotenuse > 0 && sideB !== undefined && sideB > 0 && sideB 0 && angleA 0 && angleB < 90 && Math.abs((angleA + angleB) – 90) < 0.001) {
// We need at least one side to calculate others. This case alone is insufficient.
// We'll proceed, but side calculations might be based on one of the existing sides if provided.
// If only angles are given, we can't determine scale. Mark as insufficient.
setDisplay("result", "none");
setDisplay("intermediateResults", "none");
setDisplay("copyBtn", "none");
document.getElementById("result").innerHTML = "
Need at least one side length along with angles.
";
setDisplay("result", "block");
return;
}
// Fallback for when inputs might be conflicting or insufficient after initial checks
else if (inputsUsed < 2) {
setDisplay("result", "none");
setDisplay("intermediateResults", "none");
setDisplay("copyBtn", "none");
document.getElementById("result").innerHTML = "
Insufficient valid data to calculate.
";
setDisplay("result", "block");
return;
}
// — Update Input Fields with Calculated Values —
// Only update if the original field was empty
if (hypotenuseInput.value === "") hypotenuseInput.value = calculatedHypotenuse.toFixed(4);
if (angleAInput.value === "") angleAInput.value = calculatedAngleA.toFixed(4);
if (angleBInput.value === "") angleBInput.value = calculatedAngleB.toFixed(4);
// Update intermediate values if they were not the primary inputs
if (sideAInput.value === "") sideAInput.value = calculatedSideA.toFixed(4);
if (sideBInput.value === "") sideBInput.value = calculatedSideB.toFixed(4);
// — Display Results —
getElement("resultHypotenuse").textContent = calculatedHypotenuse.toFixed(4);
getElement("resultAngleA").textContent = calculatedAngleA.toFixed(4);
getElement("resultAngleB").textContent = calculatedAngleB.toFixed(4);
var area = 0.5 * calculatedSideA * calculatedSideB;
getElement("resultArea").textContent = area.toFixed(4);
getElement("interSideA").textContent = parseFloat(sideAInput.value).toFixed(4);
getElement("interSideB").textContent = parseFloat(sideBInput.value).toFixed(4);
setDisplay("result", "block");
setDisplay("intermediateResults", "block");
setDisplay("copyBtn", "block");
// — Update Table —
var sinB = calculatedSideB / calculatedHypotenuse;
var cosB = calculatedSideA / calculatedHypotenuse;
var tanB = calculatedSideB / calculatedSideA;
getElement("sinBValue").textContent = sinB.toFixed(4);
getElement("cosBValue").textContent = cosB.toFixed(4);
getElement("tanBValue").textContent = tanB.toFixed(4);
// — Update Chart —
updateChart(calculatedSideA, calculatedSideB, calculatedHypotenuse, calculatedAngleA, calculatedAngleB);
}
function resetCalculator() {
getElement("sideA").value = "3";
getElement("sideB").value = "4";
getElement("hypotenuse").value = "";
getElement("angleA").value = "";
getElement("angleB").value = "";
getElement("sideAError").style.display = "none";
getElement("sideBError").style.display = "none";
getElement("hypotenuseError").style.display = "none";
getElement("angleAError").style.display = "none";
getElement("angleBError").style.display = "none";
setDisplay("result", "none");
setDisplay("intermediateResults", "none");
setDisplay("copyBtn", "none");
// Clear chart
if (chartInstance) {
chartInstance.destroy();
chartInstance = null;
}
var canvas = getElement('trigChart');
var ctx = canvas.getContext('2d');
ctx.clearRect(0, 0, canvas.width, canvas.height);
// Clear trig table
getElement("sinBValue").textContent = "";
getElement("cosBValue").textContent = "";
getElement("tanBValue").textContent = "";
}
function copyResults() {
var resultText = "— Right Triangle Calculation Results —\n\n";
resultText += "Inputs Provided:\n";
if (getElement("sideA").value) resultText += "- Side A: " + getElement("sideA").value + "\n";
if (getElement("sideB").value) resultText += "- Side B: " + getElement("sideB").value + "\n";
if (getElement("hypotenuse").value) resultText += "- Hypotenuse: " + getElement("hypotenuse").value + "\n";
if (getElement("angleA").value) resultText += "- Angle A: " + getElement("angleA").value + " degrees\n";
if (getElement("angleB").value) resultText += "- Angle B: " + getElement("angleB").value + " degrees\n\n";
resultText += "Calculated Values:\n";
resultText += "- Hypotenuse: " + getElement("resultHypotenuse").textContent + "\n";
resultText += "- Angle A: " + getElement("resultAngleA").textContent + " degrees\n";
resultText += "- Angle B: " + getElement("resultAngleB").textContent + " degrees\n";
resultText += "- Area: " + getElement("resultArea").textContent + "\n\n";
resultText += "Trigonometric Ratios (Angle B):\n";
resultText += "- sin(B): " + getElement("sinBValue").textContent + "\n";
resultText += "- cos(B): " + getElement("cosBValue").textContent + "\n";
resultText += "- tan(B): " + getElement("tanBValue").textContent + "\n";
try {
navigator.clipboard.writeText(resultText).then(function() {
// Feedback to user (optional)
var btn = getElement("copyBtn");
var originalText = btn.textContent;
btn.textContent = "Copied!";
setTimeout(function() {
btn.textContent = originalText;
}, 1500);
});
} catch (err) {
console.error('Failed to copy: ', err);
// Fallback for older browsers or environments where clipboard API is not available
alert("Could not copy results. Please select and copy manually.");
}
}
function updateChart(sideA, sideB, hypotenuse, angleA, angleB) {
var canvas = getElement('trigChart');
var ctx = canvas.getContext('2d');
// Clear previous chart if it exists
if (chartInstance) {
chartInstance.destroy();
}
// Adjust canvas size for better visualization if needed
canvas.width = 600;
canvas.height = 300;
var data = {
labels: ['Side A', 'Side B', 'Hypotenuse', 'Angle A (°)', 'Angle B (°)'],
datasets: [{
label: 'Length (Units)',
data: [sideA, sideB, hypotenuse, null, null], // Angles don't have 'length' units
backgroundColor: 'rgba(0, 74, 153, 0.6)',
borderColor: 'rgba(0, 74, 153, 1)',
borderWidth: 1,
yAxisID: 'y-length'
}, {
label: 'Angle (°)',
data: [null, null, null, angleA, angleB], // Sides don't have 'angle' units
backgroundColor: 'rgba(40, 167, 69, 0.6)',
borderColor: 'rgba(40, 167, 69, 1)',
borderWidth: 1,
yAxisID: 'y-angle'
}]
};
var options = {
responsive: true,
maintainAspectRatio: false, // Allows manual control of size
scales: {
x: {
grid: {
display: false // Hide x-axis grid lines for cleaner look
}
},
y-length: {
type: 'linear',
position: 'left',
beginAtZero: true,
title: {
display: true,
text: 'Length (Units)'
},
grid: {
color: 'rgba(200, 200, 200, 0.2)'
}
},
y-angle: {
type: 'linear',
position: 'right',
beginAtZero: true,
max: 90, // Angles are max 90 degrees
title: {
display: true,
text: 'Angle (°)'
},
grid: {
drawOnChartArea: false, // Only display grid lines for the primary y-axis
}
}
},
plugins: {
title: {
display: true,
text: 'Right Triangle Measurements Visualization',
font: {
size: 16
}
},
legend: {
position: 'bottom'
}
}
};
// Chart.js initialization would typically go here.
// Since we are using native canvas and not a library, we'll draw manually.
// NOTE: For a real-world application, using a library like Chart.js is highly recommended
// for robust charting. Native canvas drawing is complex.
// Below is a SIMPLIFIED conceptual drawing, not a full Chart.js replacement.
ctx.clearRect(0, 0, canvas.width, canvas.height); // Clear canvas
// Basic visualization: Bars for sides, markers for angles
var padding = 50;
var chartAreaWidth = canvas.width – 2 * padding;
var chartAreaHeight = canvas.height – 2 * padding;
// Scale lengths to fit
var maxSide = Math.max(sideA, sideB, hypotenuse);
var lengthScale = maxSide > 0 ? (chartAreaHeight * 0.8) / maxSide : 0; // Scale to fit 80% of chart height
// Scale angles to fit
var angleScale = chartAreaHeight * 0.8 / 90; // Scale to fit 80% of chart height
// Draw Side Bars
var barWidth = chartAreaWidth / 8;
var spacing = chartAreaWidth / 10;
// Side A Bar
ctx.fillStyle = 'rgba(0, 74, 153, 0.6)';
ctx.fillRect(padding + spacing, padding + chartAreaHeight – sideA * lengthScale, barWidth, sideA * lengthScale);
ctx.fillStyle = '#000′;
ctx.font = '12px Arial';
ctx.textAlign = 'center';
ctx.fillText('Side A', padding + spacing + barWidth / 2, padding + chartAreaHeight + 15);
ctx.fillText(sideA.toFixed(2), padding + spacing + barWidth / 2, padding + chartAreaHeight – sideA * lengthScale – 5);
// Side B Bar
ctx.fillStyle = 'rgba(0, 74, 153, 0.6)';
ctx.fillRect(padding + spacing * 2 + barWidth, padding + chartAreaHeight – sideB * lengthScale, barWidth, sideB * lengthScale);
ctx.fillText('Side B', padding + spacing * 2 + barWidth + barWidth / 2, padding + chartAreaHeight + 15);
ctx.fillText(sideB.toFixed(2), padding + spacing * 2 + barWidth + barWidth / 2, padding + chartAreaHeight – sideB * lengthScale – 5);
// Hypotenuse Bar
ctx.fillStyle = 'rgba(0, 74, 153, 0.6)';
ctx.fillRect(padding + spacing * 3 + barWidth * 2, padding + chartAreaHeight – hypotenuse * lengthScale, barWidth, hypotenuse * lengthScale);
ctx.fillText('Hypotenuse', padding + spacing * 3 + barWidth * 2 + barWidth / 2, padding + chartAreaHeight + 15);
ctx.fillText(hypotenuse.toFixed(2), padding + spacing * 3 + barWidth * 2 + barWidth / 2, padding + chartAreaHeight – hypotenuse * lengthScale – 5);
// Draw Angle Markers (Simplified – just placing text)
ctx.fillStyle = 'rgba(40, 167, 69, 1)';
ctx.textAlign = 'center';
// Angle A Marker
ctx.fillText('Angle A: ' + angleA.toFixed(2) + '°', padding + chartAreaWidth * 0.75, padding + chartAreaHeight * 0.5);
// Angle B Marker
ctx.fillText('Angle B: ' + angleB.toFixed(2) + '°', padding + chartAreaWidth * 0.25, padding + chartAreaHeight * 0.5);
// Add Y-axis labels manually
ctx.fillStyle = '#333';
ctx.textAlign = 'right';
ctx.font = '12px Arial';
var tickCount = 5;
for (var i = 0; i <= tickCount; i++) {
var yPos = padding + chartAreaHeight – (chartAreaHeight * 0.8 / tickCount) * i;
var value = (maxSide / tickCount) * i;
ctx.fillText(value.toFixed(1), padding – 5, yPos);
var angleYPos = padding + chartAreaHeight – (chartAreaHeight * 0.8 / tickCount) * i;
var angleValue = (90 / tickCount) * i;
ctx.fillText(angleValue.toFixed(1), canvas.width – padding + 15, angleYPos); // Right axis labels
}
// Axis Titles
ctx.save();
ctx.translate(padding – 25, padding + chartAreaHeight / 2);
ctx.rotate(-90 * Math.PI / 180);
ctx.textAlign = 'center';
ctx.fillText('Length (Units)', 0, 0);
ctx.restore();
ctx.textAlign = 'center';
ctx.fillText('Angle (°)', canvas.width – padding / 2, padding + chartAreaHeight / 2);
// Draw Axis Lines
ctx.strokeStyle = '#ccc';
ctx.lineWidth = 1;
// Left Y-axis
ctx.beginPath();
ctx.moveTo(padding, padding);
ctx.lineTo(padding, padding + chartAreaHeight);
ctx.stroke();
// Right Y-axis
ctx.beginPath();
ctx.moveTo(canvas.width – padding, padding);
ctx.lineTo(canvas.width – padding, padding + chartAreaHeight);
ctx.stroke();
// X-axis (implied by labels at bottom)
ctx.beginPath();
ctx.moveTo(padding, padding + chartAreaHeight);
ctx.lineTo(canvas.width – padding, padding + chartAreaHeight);
ctx.stroke();
// Placeholder for chart instance if using a library.
// For native canvas, we don't have a 'chartInstance' to destroy in the same way.
// We'd simply redraw on the canvas.
}
function toggleFaq(element) {
var answer = element.nextElementSibling;
if (answer.style.display === "block") {
answer.style.display = "none";
} else {
answer.style.display = "block";
}
}
// Initial calculation on page load if default values are present
document.addEventListener("DOMContentLoaded", function() {
// Trigger initial calculation if default values exist and are valid
if (getElement("sideA").value && getElement("sideB").value) {
calculateTrig();
}
});