function toRadians(degrees) {
return degrees * (Math.PI / 180);
}
function toDegrees(radians) {
return radians * (180 / Math.PI);
}
function calculateRightTriangle() {
var sideA_input = parseFloat(document.getElementById('sideA').value);
var sideB_input = parseFloat(document.getElementById('sideB').value);
var hypotenuseC_input = parseFloat(document.getElementById('hypotenuseC').value);
var angleA_input = parseFloat(document.getElementById('angleA').value);
var angleB_input = parseFloat(document.getElementById('angleB').value);
var a = isNaN(sideA_input) || sideA_input <= 0 ? null : sideA_input;
var b = isNaN(sideB_input) || sideB_input <= 0 ? null : sideB_input;
var c = isNaN(hypotenuseC_input) || hypotenuseC_input <= 0 ? null : hypotenuseC_input;
var A = isNaN(angleA_input) || angleA_input = 90 ? null : angleA_input;
var B = isNaN(angleB_input) || angleB_input = 90 ? null : angleB_input;
var inputsProvided = 0;
if (a !== null) inputsProvided++;
if (b !== null) inputsProvided++;
if (c !== null) inputsProvided++;
if (A !== null) inputsProvided++;
if (B !== null) inputsProvided++;
var errorMessage = document.getElementById('errorMessage');
errorMessage.textContent = ";
if (inputsProvided = c) throw new Error("Side A cannot be greater than or equal to Hypotenuse C.");
b = Math.sqrt(c * c – a * a);
A = toDegrees(Math.asin(a / c));
B = 90 – A;
} else if (b !== null && c !== null) { // Case 3: Side B and Hypotenuse C
if (b >= c) throw new Error("Side B cannot be greater than or equal to Hypotenuse C.");
a = Math.sqrt(c * c – b * b);
B = toDegrees(Math.asin(b / c));
A = 90 – B;
} else if (a !== null && A !== null) { // Case 4: Side A and Angle A
B = 90 – A;
c = a / Math.sin(toRadians(A));
b = a / Math.tan(toRadians(A));
} else if (a !== null && B !== null) { // Case 5: Side A and Angle B
A = 90 – B;
c = a / Math.cos(toRadians(B));
b = a * Math.tan(toRadians(B));
} else if (b !== null && A !== null) { // Case 6: Side B and Angle A
B = 90 – A;
c = b / Math.cos(toRadians(A));
a = b * Math.tan(toRadians(A));
} else if (b !== null && B !== null) { // Case 7: Side B and Angle B
A = 90 – B;
c = b / Math.sin(toRadians(B));
a = b / Math.tan(toRadians(B));
} else if (c !== null && A !== null) { // Case 8: Hypotenuse C and Angle A
B = 90 – A;
a = c * Math.sin(toRadians(A));
b = c * Math.cos(toRadians(A));
} else if (c !== null && B !== null) { // Case 9: Hypotenuse C and Angle B
A = 90 – B;
a = c * Math.cos(toRadians(B));
b = c * Math.sin(toRadians(B));
} else {
errorMessage.textContent = 'Insufficient or invalid combination of inputs. Please provide a valid pair of values.';
clearResults();
return;
}
// Final checks for consistency if more than two inputs were given
// This part is optional for a basic calculator but good for robustness
// For example, if a, b, c are all given, check if a^2 + b^2 = c^2
// For simplicity, we'll just calculate based on the first valid pair found.
if (a <= 0 || b <= 0 || c <= 0 || A <= 0 || B = 90 || B >= 90) {
throw new Error("Calculated values resulted in an impossible triangle (e.g., side length = 90). Please check your inputs.");
}
var area = 0.5 * a * b;
var perimeter = a + b + c;
document.getElementById('resultSideA').textContent = 'Side A: ' + a.toFixed(4) + ' units';
document.getElementById('resultSideB').textContent = 'Side B: ' + b.toFixed(4) + ' units';
document.getElementById('resultHypotenuseC').textContent = 'Hypotenuse C: ' + c.toFixed(4) + ' units';
document.getElementById('resultAngleA').textContent = 'Angle A: ' + A.toFixed(4) + ' degrees';
document.getElementById('resultAngleB').textContent = 'Angle B: ' + B.toFixed(4) + ' degrees';
document.getElementById('resultArea').textContent = 'Area: ' + area.toFixed(4) + ' sq. units';
document.getElementById('resultPerimeter').textContent = 'Perimeter: ' + perimeter.toFixed(4) + ' units';
} catch (e) {
errorMessage.textContent = 'Error: ' + e.message;
clearResults();
}
}
function clearResults() {
document.getElementById('resultSideA').textContent = 'Side A: ';
document.getElementById('resultSideB').textContent = 'Side B: ';
document.getElementById('resultHypotenuseC').textContent = 'Hypotenuse C: ';
document.getElementById('resultAngleA').textContent = 'Angle A: ';
document.getElementById('resultAngleB').textContent = 'Angle B: ';
document.getElementById('resultArea').textContent = 'Area: ';
document.getElementById('resultPerimeter').textContent = 'Perimeter: ';
}
function clearInputs() {
document.getElementById('sideA').value = ";
document.getElementById('sideB').value = ";
document.getElementById('hypotenuseC').value = ";
document.getElementById('angleA').value = ";
document.getElementById('angleB').value = ";
document.getElementById('errorMessage').textContent = ";
clearResults();
}
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 Properties and Formulas:
- Pythagorean Theorem: For a right triangle with legs 'a' and 'b' and hypotenuse 'c', the relationship is given by
a² + b² = c². This fundamental theorem allows us to find the length of any side if the other two are known.
- Trigonometric Ratios (SOH CAH TOA): These ratios relate the angles of a right triangle to the ratios of its sides.
- Sine (sin):
sin(angle) = Opposite / Hypotenuse
- Cosine (cos):
cos(angle) = Adjacent / Hypotenuse
- Tangent (tan):
tan(angle) = Opposite / Adjacent
These ratios are crucial for finding unknown sides or angles when one side and one acute angle are known.
- Angle Sum Property: The sum of all angles in any triangle is 180 degrees. Since one angle in a right triangle is 90 degrees, the sum of the other two acute angles (Angle A and Angle B) must be 90 degrees (
A + B = 90°).
- Area: The area of a right triangle is calculated as half the product of its two legs:
Area = (1/2) * base * height = (1/2) * a * b.
- Perimeter: The perimeter is simply the sum of the lengths of all three sides:
Perimeter = a + b + c.
How to Use This Calculator:
This Right Triangle Calculator is designed to help you find missing sides, angles, area, and perimeter of a right-angled triangle. To use it, simply input at least two known values into the corresponding fields. The calculator will then determine all other unknown properties.
- Input Fields:
- Side A (Leg): Length of one leg of the triangle.
- Side B (Leg): Length of the other leg of the triangle.
- Hypotenuse C: Length of the longest side, opposite the 90-degree angle.
- Angle A (degrees): One of the acute angles (not the 90-degree angle).
- Angle B (degrees): The other acute angle.
- Calculation: After entering your known values, click the "Calculate" button. The calculator will use the appropriate geometric and trigonometric formulas to solve for the remaining properties.
- Results: The results section will display the calculated lengths of sides, measures of angles (in degrees), the total area, and the perimeter of the triangle.
- Clear: Use the "Clear" button to reset all input fields and results.
Examples:
Let's look at some common scenarios:
Example 1: Given Two Legs
Suppose you know the two legs of a right triangle:
- Side A = 3 units
- Side B = 4 units
Input these values into the calculator. It will then calculate:
- Hypotenuse C = 5 units (from
3² + 4² = 5²)
- Angle A ≈ 36.87 degrees
- Angle B ≈ 53.13 degrees
- Area = 6 sq. units
- Perimeter = 12 units
Example 2: Given One Leg and the Hypotenuse
Consider a right triangle where:
- Side A = 6 units
- Hypotenuse C = 10 units
Input these values. The calculator will determine:
- Side B = 8 units (from
6² + 8² = 10²)
- Angle A ≈ 36.87 degrees
- Angle B ≈ 53.13 degrees
- Area = 24 sq. units
- Perimeter = 24 units
Example 3: Given One Leg and One Acute Angle
If you have:
- Side A = 7 units
- Angle A = 45 degrees
The calculator will compute:
- Angle B = 45 degrees (since
90 - 45 = 45)
- Hypotenuse C ≈ 9.90 units (from
c = a / sin(A))
- Side B = 7 units (since it's an isosceles right triangle)
- Area = 24.5 sq. units
- Perimeter ≈ 23.90 units
Applications:
Right triangles are fundamental in many fields:
- Construction and Architecture: Used for calculating roof pitches, ramp slopes, and structural stability.
- Navigation: Essential for determining distances and bearings in air and sea travel.
- Engineering: Applied in mechanics, electrical engineering, and civil engineering for force analysis, circuit design, and bridge construction.
- Physics: Used to resolve vectors into components, analyze projectile motion, and understand wave phenomena.
- Computer Graphics: Fundamental for 3D modeling and rendering.
This calculator simplifies complex trigonometric and geometric calculations, making it a valuable tool for students, educators, and professionals alike.