Right-Angled Triangle Calculator
Enter any two known values (sides can be any unit, angles in degrees) for a right-angled triangle, and this calculator will determine the remaining sides and angles. Angle C is always 90 degrees.
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padding: 20px;
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box-shadow: 0 2px 10px rgba(0,0,0,0.1);
max-width: 600px;
margin: 20px auto;
border: 1px solid #ddd;
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.trigonometric-calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 15px;
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margin-bottom: 25px;
line-height: 1.6;
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grid-template-columns: 1fr 1fr;
gap: 15px;
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.input-group {
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.input-group input[type="number"] {
padding: 10px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 16px;
width: 100%;
box-sizing: border-box;
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.calculator-inputs button {
grid-column: span 1;
padding: 12px 20px;
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color: white;
border: none;
border-radius: 5px;
font-size: 16px;
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transition: background-color 0.3s ease;
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.calculator-inputs button:last-of-type:hover {
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margin-bottom: 10px;
text-align: center;
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.calculator-results p {
margin: 5px 0;
text-align: left;
color: #155724;
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#trigError {
font-weight: bold;
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@media (max-width: 480px) {
.calculator-inputs {
grid-template-columns: 1fr;
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.calculator-inputs button {
grid-column: span 1;
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function calculateTrig() {
var sideA_input = document.getElementById('sideA').value;
var sideB_input = document.getElementById('sideB').value;
var hypotenuseC_input = document.getElementById('hypotenuseC').value;
var angleA_input = document.getElementById('angleA').value;
var angleB_input = document.getElementById('angleB').value;
var a = parseFloat(sideA_input);
var b = parseFloat(sideB_input);
var c = parseFloat(hypotenuseC_input);
var A_deg = parseFloat(angleA_input);
var B_deg = parseFloat(angleB_input);
var inputs = [];
if (!isNaN(a) && a > 0) inputs.push({id: 'a', value: a});
if (!isNaN(b) && b > 0) inputs.push({id: 'b', value: b});
if (!isNaN(c) && c > 0) inputs.push({id: 'c', value: c});
if (!isNaN(A_deg) && A_deg > 0 && A_deg 0 && B_deg < 90) inputs.push({id: 'B', value: B_deg});
var resultDiv = document.getElementById('trigResult');
var errorDiv = document.getElementById('trigError');
errorDiv.innerHTML = '';
resultDiv.innerHTML = '';
if (inputs.length !== 2) {
errorDiv.innerHTML = 'Please enter exactly two valid values (sides must be positive, angles between 0 and 90 degrees).';
return;
}
// Initialize results
var res_a = NaN, res_b = NaN, res_c = NaN, res_A_deg = NaN, res_B_deg = NaN;
// Assign known values
for (var i = 0; i = res_c) { errorDiv.innerHTML = 'Side "a" cannot be greater than or equal to hypotenuse "c".'; return; }
res_b = Math.sqrt(res_c * res_c – res_a * res_a);
res_A_deg = toDegrees(Math.asin(res_a / res_c));
res_B_deg = 90 – res_A_deg;
} else if ((input1_id === 'b' && input2_id === 'c') || (input1_id === 'c' && input2_id === 'b')) {
if (res_b >= res_c) { errorDiv.innerHTML = 'Side "b" cannot be greater than or equal to hypotenuse "c".'; return; }
res_a = Math.sqrt(res_c * res_c – res_b * res_b);
res_B_deg = toDegrees(Math.asin(res_b / res_c));
res_A_deg = 90 – res_B_deg;
}
// Case 2: One Side and One Angle Known
else if ((input1_id === 'a' && input2_id === 'A') || (input1_id === 'A' && input2_id === 'a')) {
var A_rad = toRadians(res_A_deg);
res_B_deg = 90 – res_A_deg;
res_c = res_a / Math.sin(A_rad);
res_b = res_a / Math.tan(A_rad);
} else if ((input1_id === 'a' && input2_id === 'B') || (input1_id === 'B' && input2_id === 'a')) {
var B_rad = toRadians(res_B_deg);
res_A_deg = 90 – res_B_deg;
res_c = res_a / Math.cos(B_rad);
res_b = res_a * Math.tan(B_rad);
} else if ((input1_id === 'b' && input2_id === 'A') || (input1_id === 'A' && input2_id === 'b')) {
var A_rad = toRadians(res_A_deg);
res_B_deg = 90 – res_A_deg;
res_c = res_b / Math.cos(A_rad);
res_a = res_b * Math.tan(A_rad);
} else if ((input1_id === 'b' && input2_id === 'B') || (input1_id === 'B' && input2_id === 'b')) {
var B_rad = toRadians(res_B_deg);
res_A_deg = 90 – res_B_deg;
res_c = res_b / Math.sin(B_rad);
res_a = res_b / Math.tan(B_rad);
} else if ((input1_id === 'c' && input2_id === 'A') || (input1_id === 'A' && input2_id === 'c')) {
var A_rad = toRadians(res_A_deg);
res_B_deg = 90 – res_A_deg;
res_a = res_c * Math.sin(A_rad);
res_b = res_c * Math.cos(A_rad);
} else if ((input1_id === 'c' && input2_id === 'B') || (input1_id === 'B' && input2_id === 'c')) {
var B_rad = toRadians(res_B_deg);
res_A_deg = 90 – res_B_deg;
res_a = res_c * Math.cos(B_rad);
res_b = res_c * Math.sin(B_rad);
} else {
errorDiv.innerHTML = 'Invalid combination of inputs. Please ensure you provide two distinct values that allow for a unique solution.';
return;
}
// Display results
var output = '
Calculated Triangle Properties:
';
output += 'Side a: ' + res_a.toFixed(4) + ";
output += 'Side b: ' + res_b.toFixed(4) + ";
output += 'Hypotenuse c: ' + res_c.toFixed(4) + ";
output += 'Angle A: ' + res_A_deg.toFixed(4) + ' degrees';
output += 'Angle B: ' + res_B_deg.toFixed(4) + ' degrees';
output += 'Angle C: 90 degrees';
resultDiv.innerHTML = output;
}
Understanding the Right-Angled Triangle Calculator
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. It's fundamental in fields like engineering, physics, architecture, and even video game development. Our Right-Angled Triangle Calculator simplifies the process of solving for unknown sides and angles in these specific triangles.
What is a Right-Angled Triangle?
A right-angled triangle (or right triangle) is a triangle in which one of the angles is exactly 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, which is always the longest side. The other two sides are called legs.
- Sides: We typically label the legs as 'a' and 'b', and the hypotenuse as 'c'.
- Angles: The angles opposite sides 'a', 'b', and 'c' are usually labeled 'A', 'B', and 'C' respectively. In a right triangle, Angle C is always 90 degrees. The sum of angles A and B must therefore be 90 degrees (since the sum of all angles in a triangle is 180 degrees).
Key Trigonometric Ratios (SOH CAH TOA)
The relationships between the angles and sides of a right-angled triangle are defined by three primary trigonometric ratios:
- Sine (sin): The ratio of the length of the side opposite an angle to the length of the hypotenuse.
sin(A) = Opposite / Hypotenuse = a / csin(B) = Opposite / Hypotenuse = b / c
- Cosine (cos): The ratio of the length of the side adjacent to an angle to the length of the hypotenuse.
cos(A) = Adjacent / Hypotenuse = b / ccos(B) = Adjacent / Hypotenuse = a / c
- Tangent (tan): The ratio of the length of the side opposite an angle to the length of the side adjacent to that angle.
tan(A) = Opposite / Adjacent = a / btan(B) = Opposite / Adjacent = b / a
The Pythagorean Theorem
Another crucial relationship in right-angled triangles is the Pythagorean Theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
a² + b² = c²
This theorem allows you to find the length of any side if the other two sides are known.
How to Use the Calculator
Our calculator is designed to be intuitive:
- Identify Knowns: Look at your right-angled triangle problem and identify which two values (sides or acute angles) you already know.
- Enter Values: Input these two values into the corresponding fields in the calculator. Ensure sides are positive numbers and angles are between 0 and 90 degrees (exclusive).
- Calculate: Click the "Calculate" button.
- View Results: The calculator will instantly display the lengths of the unknown sides and the measures of the unknown acute angles, along with the constant 90-degree angle.
Examples of Use
Example 1: Two Sides Known (Legs)
Imagine you have a right triangle where side 'a' is 6 units and side 'b' is 8 units. You want to find the hypotenuse 'c' and angles A and B.
- Enter '6' in "Side 'a'".
- Enter '8' in "Side 'b'".
- Click "Calculate".
Result: The calculator will show Hypotenuse 'c' = 10.0000, Angle A ≈ 36.8699 degrees, and Angle B ≈ 53.1301 degrees.
Example 2: One Side and One Angle Known
Suppose you know the hypotenuse 'c' is 15 units and Angle A is 30 degrees. You need to find sides 'a', 'b', and Angle B.
- Enter '15' in "Hypotenuse 'c'".
- Enter '30' in "Angle A".
- Click "Calculate".
Result: The calculator will show Side 'a' = 7.5000, Side 'b' ≈ 12.9904, and Angle B = 60.0000 degrees.
Example 3: One Leg and Hypotenuse Known
You have a right triangle where side 'b' is 12 units and the hypotenuse 'c' is 13 units. Find side 'a' and angles A and B.
- Enter '12' in "Side 'b'".
- Enter '13' in "Hypotenuse 'c'".
- Click "Calculate".
Result: The calculator will show Side 'a' = 5.0000, Angle A ≈ 22.6199 degrees, and Angle B ≈ 67.3801 degrees.
This calculator is a powerful tool for students, educators, and professionals alike, making complex trigonometric calculations straightforward and accessible.