function displayTrigError(message) {
document.getElementById('errorMessage').textContent = message;
document.getElementById('outputSideA').textContent = ";
document.getElementById('outputSideB').textContent = ";
document.getElementById('outputHypotenuseC').textContent = ";
document.getElementById('outputAngleA').textContent = ";
document.getElementById('outputAngleB').textContent = ";
}
function clearTrigInputs() {
document.getElementById('inputSideA').value = ";
document.getElementById('inputSideB').value = ";
document.getElementById('inputHypotenuseC').value = ";
document.getElementById('inputAngleA').value = ";
displayTrigError("); // Clear error message and results
}
function calculateTrig() {
displayTrigError("); // Clear previous errors
var sideA_val = parseFloat(document.getElementById('inputSideA').value);
var sideB_val = parseFloat(document.getElementById('inputSideB').value);
var hypotenuseC_val = parseFloat(document.getElementById('inputHypotenuseC').value);
var angleA_deg_val = parseFloat(document.getElementById('inputAngleA').value);
var inputs = { a: NaN, b: NaN, c: NaN, angleA: NaN };
var validInputsCount = 0;
if (!isNaN(sideA_val) && sideA_val > 0) { inputs.a = sideA_val; validInputsCount++; }
if (!isNaN(sideB_val) && sideB_val > 0) { inputs.b = sideB_val; validInputsCount++; }
if (!isNaN(hypotenuseC_val) && hypotenuseC_val > 0) { inputs.c = hypotenuseC_val; validInputsCount++; }
if (!isNaN(angleA_deg_val) && angleA_deg_val > 0 && angleA_deg_val < 90) { inputs.angleA = angleA_deg_val; validInputsCount++; }
if (validInputsCount 2) {
displayTrigError("Please enter exactly two values to calculate the triangle. If you enter more, the results might be inconsistent or incorrect.");
return;
}
var calcSideA = NaN, calcSideB = NaN, calcHypotenuseC = NaN, calcAngleA_deg = NaN, calcAngleB_deg = NaN;
var PI = Math.PI;
// Case 1: Side A and Side B provided
if (!isNaN(inputs.a) && !isNaN(inputs.b) && isNaN(inputs.c) && isNaN(inputs.angleA)) {
calcHypotenuseC = Math.sqrt(inputs.a * inputs.a + inputs.b * inputs.b);
calcAngleA_deg = Math.atan(inputs.a / inputs.b) * 180 / PI;
calcAngleB_deg = 90 – calcAngleA_deg;
calcSideA = inputs.a;
calcSideB = inputs.b;
}
// Case 2: Side A and Hypotenuse C provided
else if (!isNaN(inputs.a) && isNaN(inputs.b) && !isNaN(inputs.c) && isNaN(inputs.angleA)) {
if (inputs.a >= inputs.c) {
displayTrigError("Side A cannot be greater than or equal to Hypotenuse C.");
return;
}
calcSideB = Math.sqrt(inputs.c * inputs.c – inputs.a * inputs.a);
calcAngleA_deg = Math.asin(inputs.a / inputs.c) * 180 / PI;
calcAngleB_deg = 90 – calcAngleA_deg;
calcSideA = inputs.a;
calcHypotenuseC = inputs.c;
}
// Case 3: Side B and Hypotenuse C provided
else if (isNaN(inputs.a) && !isNaN(inputs.b) && !isNaN(inputs.c) && isNaN(inputs.angleA)) {
if (inputs.b >= inputs.c) {
displayTrigError("Side B cannot be greater than or equal to Hypotenuse C.");
return;
}
calcSideA = Math.sqrt(inputs.c * inputs.c – inputs.b * inputs.b);
calcAngleA_deg = Math.acos(inputs.b / inputs.c) * 180 / PI;
calcAngleB_deg = 90 – calcAngleA_deg;
calcSideB = inputs.b;
calcHypotenuseC = inputs.c;
}
// Case 4: Side A and Angle A provided
else if (!isNaN(inputs.a) && isNaN(inputs.b) && isNaN(inputs.c) && !isNaN(inputs.angleA)) {
var angleA_rad = inputs.angleA * PI / 180;
calcHypotenuseC = inputs.a / Math.sin(angleA_rad);
calcSideB = inputs.a / Math.tan(angleA_rad);
calcAngleB_deg = 90 – inputs.angleA;
calcSideA = inputs.a;
calcAngleA_deg = inputs.angleA;
}
// Case 5: Side B and Angle A provided
else if (isNaN(inputs.a) && !isNaN(inputs.b) && isNaN(inputs.c) && !isNaN(inputs.angleA)) {
var angleA_rad = inputs.angleA * PI / 180;
calcHypotenuseC = inputs.b / Math.cos(angleA_rad);
calcSideA = inputs.b * Math.tan(angleA_rad);
calcAngleB_deg = 90 – inputs.angleA;
calcSideB = inputs.b;
calcAngleA_deg = inputs.angleA;
}
// Case 6: Hypotenuse C and Angle A provided
else if (isNaN(inputs.a) && isNaN(inputs.b) && !isNaN(inputs.c) && !isNaN(inputs.angleA)) {
var angleA_rad = inputs.angleA * PI / 180;
calcSideA = inputs.c * Math.sin(angleA_rad);
calcSideB = inputs.c * Math.cos(angleA_rad);
calcAngleB_deg = 90 – inputs.angleA;
calcHypotenuseC = inputs.c;
calcAngleA_deg = inputs.angleA;
}
else {
displayTrigError("Invalid combination of inputs. Please ensure you provide exactly two values that allow for calculation.");
return;
}
document.getElementById('outputSideA').textContent = !isNaN(calcSideA) ? calcSideA.toFixed(4) + ' units' : 'N/A';
document.getElementById('outputSideB').textContent = !isNaN(calcSideB) ? calcSideB.toFixed(4) + ' units' : 'N/A';
document.getElementById('outputHypotenuseC').textContent = !isNaN(calcHypotenuseC) ? calcHypotenuseC.toFixed(4) + ' units' : 'N/A';
document.getElementById('outputAngleA').textContent = !isNaN(calcAngleA_deg) ? calcAngleA_deg.toFixed(4) + '°' : 'N/A';
document.getElementById('outputAngleB').textContent = !isNaN(calcAngleB_deg) ? calcAngleB_deg.toFixed(4) + '°' : 'N/A';
}
.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
padding: 25px;
max-width: 600px;
margin: 30px auto;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
font-size: 1.8em;
}
.calculator-content p {
margin-bottom: 15px;
line-height: 1.6;
color: #555;
}
.input-group {
margin-bottom: 15px;
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 7px;
font-weight: bold;
color: #444;
font-size: 0.95em;
}
.input-group input[type="number"] {
padding: 10px 12px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 1em;
width: 100%;
box-sizing: border-box;
transition: border-color 0.3s ease;
}
.input-group input[type="number"]:focus {
border-color: #007bff;
outline: none;
box-shadow: 0 0 0 3px rgba(0, 123, 255, 0.25);
}
.calculator-actions {
display: flex;
justify-content: center;
gap: 15px;
margin-top: 25px;
margin-bottom: 20px;
}
.calculate-button, .clear-button {
padding: 12px 25px;
border: none;
border-radius: 5px;
font-size: 1.05em;
cursor: pointer;
transition: background-color 0.3s ease, transform 0.2s ease;
flex-grow: 1;
max-width: 150px;
}
.calculate-button {
background-color: #007bff;
color: white;
}
.calculate-button:hover {
background-color: #0056b3;
transform: translateY(-2px);
}
.clear-button {
background-color: #6c757d;
color: white;
}
.clear-button:hover {
background-color: #5a6268;
transform: translateY(-2px);
}
.error-message {
color: #dc3545;
text-align: center;
margin-top: 15px;
margin-bottom: 15px;
font-weight: bold;
min-height: 20px; /* Ensure space even when empty */
}
.result-section {
background-color: #e9f7ff;
border: 1px solid #b3e0ff;
border-radius: 8px;
padding: 20px;
margin-top: 25px;
}
.result-section h3 {
color: #0056b3;
margin-top: 0;
margin-bottom: 15px;
font-size: 1.4em;
text-align: center;
}
.result-section p {
margin-bottom: 10px;
font-size: 1.1em;
color: #333;
}
.result-section p strong {
color: #003d7a;
}
.result-section span {
font-weight: normal;
color: #000;
}
Understanding Trigonometry and Right-Angled Triangles
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. It's particularly powerful when dealing with right-angled triangles, which are triangles containing one 90-degree angle. This calculator helps you quickly find missing sides or angles of a right-angled triangle given just two pieces of information.
Key Concepts of Right-Angled Triangles
In a right-angled triangle, the side opposite the right angle is called the hypotenuse. It is always the longest side. The other two sides are called legs. When referring to an acute angle (an angle less than 90 degrees), one leg is opposite to it, and the other is adjacent to it.
The Pythagorean Theorem
A fundamental relationship in right-angled triangles is the Pythagorean Theorem, which states: a² + b² = c². Here, 'a' and 'b' are the lengths of the two legs, and 'c' is the length of the hypotenuse. This theorem allows you to find the length of any side if the other two are known.
Trigonometric Ratios (SOH CAH TOA)
The three primary trigonometric ratios—Sine, Cosine, and Tangent—relate the angles of a right-angled triangle to the ratios of its side lengths. A common mnemonic to remember these is SOH CAH TOA:
- SOH: Sine = Opposite / Hypotenuse
- CAH: Cosine = Adjacent / Hypotenuse
- TOA: Tangent = Opposite / Adjacent
These ratios, along with their inverse functions (arcsin, arccos, arctan), allow you to calculate unknown angles or sides when you have a combination of one angle and one side, or two sides.
How to Use the Right-Angled Triangle Calculator
Our calculator simplifies these complex calculations. To use it:
- Identify Your Knowns: Look at your right-angled triangle and determine which two values you already know. These could be two sides (Side A, Side B, or Hypotenuse C) or one side and one acute angle (Angle A).
- Input Values: Enter these two known values into the corresponding fields in the calculator. Ensure Angle A is entered in degrees.
- Calculate: Click the "Calculate" button. The calculator will automatically determine the remaining side lengths and angles.
- Review Results: The results section will display the calculated values for the missing sides and angles, with angles in degrees and sides in generic "units".
Important: You must enter exactly two values for the calculator to function correctly. Entering fewer than two or more than two values may result in an error message or incorrect calculations.
Examples of Use
Example 1: Given Two Legs
Imagine you have a right-angled triangle where Side A (opposite to Angle A) is 3 units and Side B (adjacent to Angle A) is 4 units.
- Input Side A:
3
- Input Side B:
4
- Click "Calculate"
Results:
- Hypotenuse (C):
5.0000 units (from Pythagorean theorem: 3² + 4² = 9 + 16 = 25, √25 = 5)
- Angle A:
36.8699° (from tan(A) = 3/4, A = arctan(0.75))
- Angle B:
53.1301° (from 90° – Angle A)
Example 2: Given One Leg and an Angle
Suppose you know Side A is 5 units and Angle A is 30 degrees.
- Input Side A:
5
- Input Angle A:
30
- Click "Calculate"
Results:
- Hypotenuse (C):
10.0000 units (from sin(30°) = 5 / C, C = 5 / sin(30°))
- Side B:
8.6603 units (from tan(30°) = 5 / B, B = 5 / tan(30°))
- Angle B:
60.0000° (from 90° – 30°)
Example 3: Given Hypotenuse and an Angle
You have a hypotenuse of 10 units and Angle A is 60 degrees.
- Input Hypotenuse (C):
10
- Input Angle A:
60
- Click "Calculate"
Results:
- Side A:
8.6603 units (from sin(60°) = A / 10, A = 10 * sin(60°))
- Side B:
5.0000 units (from cos(60°) = B / 10, B = 10 * cos(60°))
- Angle B:
30.0000° (from 90° – 60°)
This calculator is a valuable tool for students, engineers, architects, and anyone needing to solve right-angled triangle problems quickly and accurately.