Instructions: Enter any two values (including at least one side) to calculate the remaining sides, angles, area, and perimeter.
Results
Side a:–
Side b:–
Hypotenuse c:–
Angle A:–°
Angle B:–°
Angle C: 90°
Area:–
Perimeter:–
function calculateRightTriangle() {
var a = parseFloat(document.getElementById('side_a').value);
var b = parseFloat(document.getElementById('side_b').value);
var c = parseFloat(document.getElementById('side_c').value);
var angleA = parseFloat(document.getElementById('angle_a').value);
var angleB = parseFloat(document.getElementById('angle_b').value);
var radToDeg = 180 / Math.PI;
var degToRad = Math.PI / 180;
var results = null;
// Priority Logic based on inputs provided
if (!isNaN(a) && !isNaN(b)) {
c = Math.sqrt(a * a + b * b);
angleA = Math.atan(a / b) * radToDeg;
angleB = 90 – angleA;
} else if (!isNaN(a) && !isNaN(c)) {
if (a >= c) { alert("Hypotenuse must be longer than side a."); return; }
b = Math.sqrt(c * c – a * a);
angleA = Math.asin(a / c) * radToDeg;
angleB = 90 – angleA;
} else if (!isNaN(b) && !isNaN(c)) {
if (b >= c) { alert("Hypotenuse must be longer than side b."); return; }
a = Math.sqrt(c * c – b * b);
angleA = Math.acos(b / c) * radToDeg;
angleB = 90 – angleA;
} else if (!isNaN(a) && !isNaN(angleA)) {
if (angleA >= 90) { alert("Angle must be less than 90°."); return; }
c = a / Math.sin(angleA * degToRad);
b = a / Math.tan(angleA * degToRad);
angleB = 90 – angleA;
} else if (!isNaN(a) && !isNaN(angleB)) {
if (angleB >= 90) { alert("Angle must be less than 90°."); return; }
c = a / Math.cos(angleB * degToRad);
b = a * Math.tan(angleB * degToRad);
angleA = 90 – angleB;
} else if (!isNaN(b) && !isNaN(angleA)) {
if (angleA >= 90) { alert("Angle must be less than 90°."); return; }
c = b / Math.cos(angleA * degToRad);
a = b * Math.tan(angleA * degToRad);
angleB = 90 – angleA;
} else if (!isNaN(b) && !isNaN(angleB)) {
if (angleB >= 90) { alert("Angle must be less than 90°."); return; }
c = b / Math.sin(angleB * degToRad);
a = b / Math.tan(angleB * degToRad);
angleA = 90 – angleB;
} else if (!isNaN(c) && !isNaN(angleA)) {
if (angleA >= 90) { alert("Angle must be less than 90°."); return; }
a = c * Math.sin(angleA * degToRad);
b = c * Math.cos(angleA * degToRad);
angleB = 90 – angleA;
} else if (!isNaN(c) && !isNaN(angleB)) {
if (angleB >= 90) { alert("Angle must be less than 90°."); return; }
a = c * Math.cos(angleB * degToRad);
b = c * Math.sin(angleB * degToRad);
angleA = 90 – angleB;
} else {
alert("Please provide at least two values, including at least one side.");
return;
}
var area = (a * b) / 2;
var perimeter = a + b + c;
document.getElementById('res_side_a').innerText = a.toFixed(4);
document.getElementById('res_side_b').innerText = b.toFixed(4);
document.getElementById('res_side_c').innerText = c.toFixed(4);
document.getElementById('res_angle_a').innerText = angleA.toFixed(4);
document.getElementById('res_angle_b').innerText = angleB.toFixed(4);
document.getElementById('res_area').innerText = area.toFixed(4);
document.getElementById('res_perimeter').innerText = perimeter.toFixed(4);
document.getElementById('triangle-results').style.display = 'block';
}
function resetTriangleFields() {
document.getElementById('side_a').value = ";
document.getElementById('side_b').value = ";
document.getElementById('side_c').value = ";
document.getElementById('angle_a').value = ";
document.getElementById('angle_b').value = ";
document.getElementById('triangle-results').style.display = 'none';
}
Understanding Right Triangle Calculations
A right triangle is a specific type of triangle where one angle is exactly 90 degrees (a right angle). Because of this unique property, the relationship between its sides and angles is governed by consistent mathematical laws, primarily the Pythagorean Theorem and Trigonometric ratios.
The Pythagorean Theorem
This is the most fundamental rule for right triangles. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
Formula: a² + b² = c²
Trigonometric Functions (SOH CAH TOA)
When you know one side and one acute angle, you can find all other measurements using sine, cosine, and tangent:
Sine (sin): Opposite / Hypotenuse
Cosine (cos): Adjacent / Hypotenuse
Tangent (tan): Opposite / Adjacent
Practical Example: Solving for the Hypotenuse
Suppose you are building a ramp that must be 3 feet high (side a) and 4 feet long along the ground (side b). To find the length of the ramp surface (hypotenuse c):
Square the legs: 3² = 9 and 4² = 16.
Add them together: 9 + 16 = 25.
Take the square root: √25 = 5.
The ramp length is 5 feet.
Key Terms to Know
Term
Definition
Legs (a & b)
The two sides that meet at the 90° angle.
Hypotenuse (c)
The longest side, located opposite the right angle.
Area
The space inside the triangle, calculated as (base × height) / 2.
Perimeter
The total distance around the triangle (a + b + c).