function toRadians(degrees) {
return degrees * (Math.PI / 180);
}
function toDegrees(radians) {
return radians * (180 / Math.PI);
}
function calculateRightTriangle() {
var sideA_val = parseFloat(document.getElementById('sideAInput').value);
var sideB_val = parseFloat(document.getElementById('sideBInput').value);
var hypotenuseC_val = parseFloat(document.getElementById('hypotenuseCInput').value);
var angleA_deg_val = parseFloat(document.getElementById('angleAInput').value);
var angleB_deg_val = parseFloat(document.getElementById('angleBInput').value);
var resultSideA = document.getElementById('resultSideA');
var resultSideB = document.getElementById('resultSideB');
var resultHypotenuseC = document.getElementById('resultHypotenuseC');
var resultAngleA = document.getElementById('resultAngleA');
var resultAngleB = document.getElementById('resultAngleB');
var resultError = document.getElementById('resultError');
resultSideA.textContent = ";
resultSideB.textContent = ";
resultHypotenuseC.textContent = ";
resultAngleA.textContent = ";
resultAngleB.textContent = ";
resultError.textContent = ";
var validInputs = [];
if (!isNaN(sideA_val) && sideA_val > 0) validInputs.push({ type: 'sideA', value: sideA_val });
if (!isNaN(sideB_val) && sideB_val > 0) validInputs.push({ type: 'sideB', value: sideB_val });
if (!isNaN(hypotenuseC_val) && hypotenuseC_val > 0) validInputs.push({ type: 'hypotenuseC', value: hypotenuseC_val });
if (!isNaN(angleA_deg_val) && angleA_deg_val > 0 && angleA_deg_val 0 && angleB_deg_val = c) { resultError.textContent = 'Side \'a\' must be less than Hypotenuse \'c\'.'; return; }
b = Math.sqrt(c * c – a * a);
A_deg = toDegrees(Math.asin(a / c));
B_deg = 90 – A_deg;
break;
case 'hypotenuseC-sideB':
b = input1.type === 'sideB' ? input1.value : input2.value;
c = input1.type === 'hypotenuseC' ? input1.value : input2.value;
if (b >= c) { resultError.textContent = 'Side \'b\' must be less than Hypotenuse \'c\'.'; return; }
a = Math.sqrt(c * c – b * b);
B_deg = toDegrees(Math.asin(b / c));
A_deg = 90 – B_deg;
break;
case 'angleA-sideA':
A_deg = input1.type === 'angleA' ? input1.value : input2.value;
a = input1.type === 'sideA' ? input1.value : input2.value;
B_deg = 90 – A_deg;
var A_rad = toRadians(A_deg);
c = a / Math.sin(A_rad);
b = a / Math.tan(A_rad);
break;
case 'angleB-sideA':
B_deg = input1.type === 'angleB' ? input1.value : input2.value;
a = input1.type === 'sideA' ? input1.value : input2.value;
A_deg = 90 – B_deg;
var B_rad = toRadians(B_deg);
c = a / Math.cos(B_rad);
b = a * Math.tan(B_rad);
break;
case 'angleA-sideB':
A_deg = input1.type === 'angleA' ? input1.value : input2.value;
b = input1.type === 'sideB' ? input1.value : input2.value;
B_deg = 90 – A_deg;
var A_rad = toRadians(A_deg);
c = b / Math.cos(A_rad);
a = b * Math.tan(A_rad);
break;
case 'angleB-sideB':
B_deg = input1.type === 'angleB' ? input1.value : input2.value;
b = input1.type === 'sideB' ? input1.value : input2.value;
A_deg = 90 – B_deg;
var B_rad = toRadians(B_deg);
c = b / Math.sin(B_rad);
a = b / Math.tan(B_rad);
break;
case 'angleA-hypotenuseC':
A_deg = input1.type === 'angleA' ? input1.value : input2.value;
c = input1.type === 'hypotenuseC' ? input1.value : input2.value;
B_deg = 90 – A_deg;
var A_rad = toRadians(A_deg);
a = c * Math.sin(A_rad);
b = c * Math.cos(A_rad);
break;
case 'angleB-hypotenuseC':
B_deg = input1.type === 'angleB' ? input1.value : input2.value;
c = input1.type === 'hypotenuseC' ? input1.value : input2.value;
A_deg = 90 – B_deg;
var B_rad = toRadians(B_deg);
a = c * Math.cos(B_rad);
b = c * Math.sin(B_rad);
break;
default:
resultError.textContent = 'An unexpected combination of inputs was provided. Please check your entries.';
return;
}
setResults(a, b, c, A_deg, B_deg);
}
function clearRightTriangle() {
document.getElementById('sideAInput').value = ";
document.getElementById('sideBInput').value = ";
document.getElementById('hypotenuseCInput').value = ";
document.getElementById('angleAInput').value = ";
document.getElementById('angleBInput').value = ";
document.getElementById('resultSideA').textContent = ";
document.getElementById('resultSideB').textContent = ";
document.getElementById('resultHypotenuseC').textContent = ";
document.getElementById('resultAngleA').textContent = ";
document.getElementById('resultAngleB').textContent = ";
document.getElementById('resultError').textContent = ";
}
.right-triangle-calculator {
font-family: Arial, sans-serif;
background-color: #f9f9f9;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
box-shadow: 0 2px 4px rgba(0,0,0,0.1);
}
.right-triangle-calculator h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
}
.right-triangle-calculator p {
color: #555;
line-height: 1.6;
}
.calculator-inputs label {
display: block;
margin-bottom: 5px;
color: #333;
font-weight: bold;
}
.calculator-inputs input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
margin-bottom: 15px;
border: 1px solid #ddd;
border-radius: 4px;
box-sizing: border-box;
}
.right-triangle-calculator button {
background-color: #007bff;
color: white;
padding: 10px 15px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
margin-right: 10px;
}
.right-triangle-calculator button:hover {
background-color: #0056b3;
}
.right-triangle-calculator button:last-of-type {
background-color: #6c757d;
}
.right-triangle-calculator button:last-of-type:hover {
background-color: #5a6268;
}
.calculator-results {
background-color: #e9ecef;
padding: 15px;
border-radius: 4px;
border: 1px solid #ced4da;
}
.calculator-results h3 {
color: #333;
margin-top: 0;
border-bottom: 1px solid #ccc;
padding-bottom: 10px;
margin-bottom: 10px;
}
.calculator-results p {
margin-bottom: 5px;
color: #333;
}
.calculator-results span {
font-weight: bold;
color: #007bff;
}
Understanding the Right Triangle and its Angles
A right triangle is a fundamental shape in geometry, characterized by one angle measuring exactly 90 degrees (a right angle). The sides of a right triangle have specific names and relationships that are crucial for many mathematical and real-world applications, from construction and engineering to navigation and astronomy.
Key Components of a Right Triangle:
- Right Angle (C): Always 90 degrees.
- Hypotenuse (c): The longest side of the triangle, always opposite the right angle.
- Legs (a and b): The two shorter sides that form the right angle. Side 'a' is typically opposite Angle A, and Side 'b' is opposite Angle B.
- Acute Angles (A and B): The other two angles, both of which are less than 90 degrees. The sum of Angle A and Angle B is always 90 degrees.
The Power of Trigonometry: SOH CAH TOA
To find unknown sides or angles in a right triangle, we use trigonometric ratios, often remembered by the acronym SOH CAH TOA:
- SOH: Sine = Opposite / Hypotenuse (
sin(Angle) = Opposite Side / Hypotenuse)
- CAH: Cosine = Adjacent / Hypotenuse (
cos(Angle) = Adjacent Side / Hypotenuse)
- TOA: Tangent = Opposite / Adjacent (
tan(Angle) = Opposite Side / Adjacent Side)
These ratios allow us to relate the angles of a right triangle to the lengths of its sides. For example, if you know the length of the side opposite an angle and the hypotenuse, you can find the angle using the inverse sine function (arcsin or sin-1).
The Pythagorean Theorem
Another cornerstone of right triangle calculations is the Pythagorean Theorem, which states: a² + b² = c². This theorem relates the lengths of the two legs (a and b) to the length of the hypotenuse (c). If you know any two sides of a right triangle, you can always find the third side using this formula.
How to Use the Right Triangle Angle Calculator
Our Right Triangle Angle Calculator simplifies these complex calculations. To use it:
- Identify Known Values: Look at your right triangle and determine which two values (sides or angles) you already know.
- Enter Values: Input these two values into the corresponding fields in the calculator. For angles, ensure they are in degrees and between 0 and 90.
- Click "Calculate": The calculator will instantly compute the remaining side lengths and angle measures.
- Review Results: The results section will display all calculated values, including Angle A, Angle B, Side 'a', Side 'b', and Hypotenuse 'c'.
Practical Examples:
Let's look at a few scenarios:
Example 1: Known Sides 'a' and 'b'
Imagine you have a right triangle where Side 'a' is 3 units and Side 'b' is 4 units.
- Input: Side 'a' = 3, Side 'b' = 4
- Calculation:
- Hypotenuse 'c' = √(3² + 4²) = √(9 + 16) = √25 = 5
- Angle A = arctan(3/4) ≈ 36.87°
- Angle B = 90° – 36.87° ≈ 53.13°
- Output: Side 'a' = 3.000, Side 'b' = 4.000, Hypotenuse 'c' = 5.000, Angle A ≈ 36.87°, Angle B ≈ 53.13°
Example 2: Known Hypotenuse 'c' and Angle A
Suppose you have a right triangle with a Hypotenuse 'c' of 10 units and Angle A is 30 degrees.
- Input: Hypotenuse 'c' = 10, Angle A = 30
- Calculation:
- Angle B = 90° – 30° = 60°
- Side 'a' = 10 * sin(30°) = 10 * 0.5 = 5
- Side 'b' = 10 * cos(30°) = 10 * 0.866025 ≈ 8.660
- Output: Side 'a' = 5.000, Side 'b' ≈ 8.660, Hypotenuse 'c' = 10.000, Angle A = 30.00°, Angle B = 60.00°
Example 3: Known Side 'b' and Angle B
Consider a right triangle where Side 'b' is 7 units and Angle B is 45 degrees.
- Input: Side 'b' = 7, Angle B = 45
- Calculation:
- Angle A = 90° – 45° = 45°
- Hypotenuse 'c' = 7 / sin(45°) = 7 / 0.707106 ≈ 9.899
- Side 'a' = 7 / tan(45°) = 7 / 1 = 7
- Output: Side 'a' = 7.000, Side 'b' = 7.000, Hypotenuse 'c' ≈ 9.899, Angle A = 45.00°, Angle B = 45.00°
This calculator is an invaluable tool for students, educators, and professionals who need to quickly and accurately solve right triangle problems.