Right Triangle Calculator
Results:
Side 'a':
Side 'b':
Hypotenuse 'c':
Angle 'A':
Angle 'B':
Angle 'C': 90°
function calculateRightTriangle() {
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 errorDiv = document.getElementById('errorMessages');
errorDiv.innerHTML = "; // Clear previous errors
var known = {
a: sideA_input === " ? null : parseFloat(sideA_input),
b: sideB_input === " ? null : parseFloat(sideB_input),
c: hypotenuseC_input === " ? null : parseFloat(hypotenuseC_input),
A: angleA_input === " ? null : parseFloat(angleA_input),
B: angleB_input === " ? null : parseFloat(angleB_input)
};
var numKnown = 0;
var hasSide = false;
for (var key in known) {
if (known[key] !== null) {
if (isNaN(known[key])) {
errorDiv.innerHTML = 'Please enter valid numbers for all inputs.';
displayResults(null, null, null, null, null);
return;
}
if (known[key] = 90 && (key === 'A' || key === 'B')) {
errorDiv.innerHTML = 'Acute angles must be less than 90 degrees.';
displayResults(null, null, null, null, null);
return;
}
numKnown++;
if (key === 'a' || key === 'b' || key === 'c') {
hasSide = true;
}
}
}
if (numKnown 0.001) {
errorDiv.innerHTML = 'Provided angles A and B do not sum to 90 degrees.';
displayResults(null, null, null, null, null);
return;
}
}
if (known.a !== null && known.c !== null && known.a >= known.c) {
errorDiv.innerHTML = 'Side \'a\' cannot be greater than or equal to hypotenuse \'c\'.';
displayResults(null, null, null, null, null);
return;
}
if (known.b !== null && known.c !== null && known.b >= known.c) {
errorDiv.innerHTML = 'Side \'b\' cannot be greater than or equal to hypotenuse \'c\'.';
displayResults(null, null, null, null, null);
return;
}
if (known.a !== null && known.b !== null && known.c !== null) {
if (Math.abs(known.a * known.a + known.b * known.b – known.c * known.c) > 0.001) {
errorDiv.innerHTML = 'Provided sides a, b, and c do not satisfy the Pythagorean theorem.';
displayResults(null, null, null, null, null);
return;
}
}
// Convert known angles to radians for internal calculations
if (known.A !== null) known.A_rad = known.A * Math.PI / 180;
if (known.B !== null) known.B_rad = known.B * Math.PI / 180;
var solved = false;
var iterations = 0;
var maxIterations = 10; // Prevent infinite loops
while (!solved && iterations = known.c) { errorDiv.innerHTML = 'Side \'a\' cannot be greater than or equal to hypotenuse \'c\'.'; displayResults(null, null, null, null, null); return; }
known.b = Math.sqrt(known.c * known.c – known.a * known.a); changed = true;
}
if (known.b !== null && known.c !== null && known.a === null) {
if (known.b >= known.c) { errorDiv.innerHTML = 'Side \'b\' cannot be greater than or equal to hypotenuse \'c\'.'; displayResults(null, null, null, null, null); return; }
known.a = Math.sqrt(known.c * known.c – known.b * known.b); changed = true;
}
// 3. Find missing sides/angles using trigonometry
// Using angle A
if (known.A !== null && known.A_rad !== null) {
if (known.a !== null && known.c === null) { known.c = known.a / Math.sin(known.A_rad); changed = true; }
if (known.a !== null && known.b === null) { known.b = known.a / Math.tan(known.A_rad); changed = true; }
if (known.b !== null && known.a === null) { known.a = known.b * Math.tan(known.A_rad); changed = true; }
if (known.b !== null && known.c === null) { known.c = known.b / Math.cos(known.A_rad); changed = true; }
if (known.c !== null && known.a === null) { known.a = known.c * Math.sin(known.A_rad); changed = true; }
if (known.c !== null && known.b === null) { known.b = known.c * Math.cos(known.A_rad); changed = true; }
}
// Using angle B
if (known.B !== null && known.B_rad !== null) {
if (known.b !== null && known.c === null) { known.c = known.b / Math.sin(known.B_rad); changed = true; }
if (known.b !== null && known.a === null) { known.a = known.b / Math.tan(known.B_rad); changed = true; }
if (known.a !== null && known.b === null) { known.b = known.a * Math.tan(known.B_rad); changed = true; }
if (known.a !== null && known.c === null) { known.c = known.a / Math.cos(known.B_rad); changed = true; }
if (known.c !== null && known.b === null) { known.b = known.c * Math.sin(known.B_rad); changed = true; }
if (known.c !== null && known.a === null) { known.a = known.c * Math.cos(known.B_rad); changed = true; }
}
// 4. Find missing angles from sides
if (known.a !== null && known.c !== null && known.A === null) {
if (known.a / known.c > 1) { errorDiv.innerHTML = 'Invalid side lengths for angle A calculation (a/c > 1).'; displayResults(null, null, null, null, null); return; }
known.A_rad = Math.asin(known.a / known.c); known.A = known.A_rad * 180 / Math.PI; changed = true;
}
if (known.b !== null && known.c !== null && known.B === null) {
if (known.b / known.c > 1) { errorDiv.innerHTML = 'Invalid side lengths for angle B calculation (b/c > 1).'; displayResults(null, null, null, null, null); return; }
known.B_rad = Math.asin(known.b / known.c); known.B = known.B_rad * 180 / Math.PI; changed = true;
}
if (known.a !== null && known.b !== null && known.A === null) { known.A_rad = Math.atan(known.a / known.b); known.A = known.A_rad * 180 / Math.PI; changed = true; }
if (known.a !== null && known.b !== null && known.B === null) { known.B_rad = Math.atan(known.b / known.a); known.B = known.B_rad * 180 / Math.PI; changed = true; }
if (!changed) {
solved = true; // No more changes were made in this iteration
}
iterations++;
}
// Final check if all values are determined
if (known.a === null || known.b === null || known.c === null || known.A === null || known.B === null) {
errorDiv.innerHTML = 'Not enough information provided to solve the triangle completely. Please provide at least two values, including at least one side.';
displayResults(null, null, null, null, null);
return;
}
displayResults(known.a, known.b, known.c, known.A, known.B);
}
function displayResults(a, b, c, A, B) {
document.getElementById('resultSideA').innerText = a !== null ? a.toFixed(4) : 'N/A';
document.getElementById('resultSideB').innerText = b !== null ? b.toFixed(4) : 'N/A';
document.getElementById('resultHypotenuseC').innerText = c !== null ? c.toFixed(4) : 'N/A';
document.getElementById('resultAngleA').innerText = A !== null ? A.toFixed(4) + '°' : 'N/A';
document.getElementById('resultAngleB').innerText = B !== null ? B.toFixed(4) + '°' : 'N/A';
}
function clearInputs() {
document.getElementById('sideA').value = ";
document.getElementById('sideB').value = ";
document.getElementById('hypotenuseC').value = ";
document.getElementById('angleA').value = ";
document.getElementById('angleB').value = ";
document.getElementById('errorMessages').innerHTML = ";
displayResults(null, null, null, null, null);
}
.calculator-container {
background-color: #f9f9f9;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
font-family: Arial, sans-serif;
}
.calculator-inputs .form-group {
margin-bottom: 15px;
}
.calculator-inputs label {
display: block;
margin-bottom: 5px;
font-weight: bold;
}
.calculator-inputs input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.calculator-inputs button {
background-color: #007bff;
color: white;
padding: 10px 15px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
margin-right: 10px;
}
.calculator-inputs button:hover {
background-color: #0056b3;
}
.calculator-results {
margin-top: 20px;
padding-top: 15px;
border-top: 1px solid #eee;
}
.calculator-results h3 {
color: #333;
margin-top: 0;
}
.calculator-results p {
margin-bottom: 8px;
line-height: 1.5;
}
.calculator-results strong {
color: #555;
}
Understanding the Right Triangle Calculator
A right triangle is a special type of triangle that has one angle measuring exactly 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and it is always the longest side. The other two sides are called legs.
Key Concepts:
- Sides: We typically label the legs as 'a' and 'b', and the hypotenuse as 'c'. Side 'a' is opposite angle 'A', and side 'b' is opposite angle 'B'. Angle 'C' is always 90 degrees.
- Pythagorean Theorem: For any right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This is expressed as:
a² + b² = c².
- Trigonometric Ratios (SOH CAH TOA): These ratios relate the angles of a right triangle to the lengths of its sides:
- Sine (sin):
sin(angle) = Opposite / Hypotenuse
- Cosine (cos):
cos(angle) = Adjacent / Hypotenuse
- Tangent (tan):
tan(angle) = Opposite / Adjacent
For angle A: sin(A) = a/c, cos(A) = b/c, tan(A) = a/b.
For angle B: sin(B) = b/c, cos(B) = a/c, tan(B) = b/a.
- Angle Sum Property: The sum of all angles in any triangle is 180 degrees. Since angle C is 90 degrees, the sum of the two acute angles (A and B) must be 90 degrees:
A + B = 90°.
How the Calculator Works:
This Right Triangle Calculator allows you to find the missing sides and angles of a right triangle by providing at least two known values. You must provide at least one side length. The calculator uses the Pythagorean theorem and trigonometric functions to solve for the unknowns.
Simply enter the values you know into the corresponding fields (Side 'a', Side 'b', Hypotenuse 'c', Angle 'A', Angle 'B'). Leave the fields you want to calculate blank. Click "Calculate" to see the results.
Examples:
Example 1: Given Two Legs
Suppose you know the lengths of the two legs:
- Side 'a' = 3
- Side 'b' = 4
The calculator will determine:
- Hypotenuse 'c' =
sqrt(3² + 4²) = sqrt(9 + 16) = sqrt(25) = 5
- Angle 'A' =
atan(3/4) ≈ 36.87°
- Angle 'B' =
90° - 36.87° = 53.13°
Example 2: Given One Leg and the Hypotenuse
Suppose you know one leg and the hypotenuse:
- Side 'a' = 6
- Hypotenuse 'c' = 10
The calculator will determine:
- Side 'b' =
sqrt(10² - 6²) = sqrt(100 - 36) = sqrt(64) = 8
- Angle 'A' =
asin(6/10) = asin(0.6) ≈ 36.87°
- Angle 'B' =
90° - 36.87° = 53.13°
Example 3: Given One Leg and One Acute Angle
Suppose you know one leg and one acute angle:
- Side 'a' = 7
- Angle 'A' = 45°
The calculator will determine:
- Angle 'B' =
90° - 45° = 45°
- Hypotenuse 'c' =
a / sin(A) = 7 / sin(45°) ≈ 7 / 0.7071 ≈ 9.8995
- Side 'b' =
a / tan(A) = 7 / tan(45°) = 7 / 1 = 7
This calculator is a valuable tool for students, engineers, architects, and anyone working with geometric problems involving right triangles.