Please ensure the Hypotenuse is the longest side and all inputs are positive numbers.
function updateLabels() {
var method = document.getElementById("calcMethod").value;
var l1 = document.getElementById("label1");
var l2 = document.getElementById("label2");
var v1 = document.getElementById("val1");
var v2 = document.getElementById("val2");
v1.value = "";
v2.value = "";
document.getElementById("triangleResult").style.display = "none";
document.getElementById("errorBox").style.display = "none";
if (method === "ab") {
l1.innerText = "Opposite Side (a):";
l2.innerText = "Adjacent Side (b):";
} else if (method === "ac") {
l1.innerText = "Opposite Side (a):";
l2.innerText = "Hypotenuse (c):";
} else {
l1.innerText = "Adjacent Side (b):";
l2.innerText = "Hypotenuse (c):";
}
}
function calculateTriangle() {
var method = document.getElementById("calcMethod").value;
var v1 = parseFloat(document.getElementById("val1").value);
var v2 = parseFloat(document.getElementById("val2").value);
var resA, resB, resS, error = false;
if (isNaN(v1) || isNaN(v2) || v1 <= 0 || v2 = v2) { error = true; } else {
resA = Math.asin(v1 / v2) * (180 / Math.PI);
resB = 90 – resA;
resS = Math.sqrt(Math.pow(v2, 2) – Math.pow(v1, 2));
}
} else if (method === "bc") {
// b and c known
if (v1 >= v2) { error = true; } else {
resA = Math.acos(v1 / v2) * (180 / Math.PI);
resB = 90 – resA;
resS = Math.sqrt(Math.pow(v2, 2) – Math.pow(v1, 2));
}
}
}
if (error) {
document.getElementById("errorBox").style.display = "block";
document.getElementById("triangleResult").style.display = "none";
} else {
document.getElementById("errorBox").style.display = "none";
document.getElementById("triangleResult").style.display = "block";
document.getElementById("resAngleA").innerText = resA.toFixed(2);
document.getElementById("resAngleB").innerText = resB.toFixed(2);
document.getElementById("resSide").innerText = resS.toFixed(2);
}
}
Understanding Right Triangle Calculations
A right triangle is a triangle in which one angle is exactly 90 degrees (a right angle). Because the sum of all angles in any triangle must be 180 degrees, the other two angles must add up to 90 degrees. These two angles are known as complementary angles.
Fundamental Trigonometric Ratios
To find the missing angles of a right triangle, we use trigonometric functions based on the ratios of the side lengths. The three primary functions are:
Sine (sin): Opposite / Hypotenuse
Cosine (cos): Adjacent / Hypotenuse
Tangent (tan): Opposite / Adjacent
The Hypotenuse is always the longest side, located opposite the 90-degree angle. The Opposite and Adjacent sides are relative to the angle you are trying to calculate.
Step-by-Step Calculation Example
Imagine you have a ladder leaning against a wall. The ladder is 10 feet long (Hypotenuse), and it reaches 8 feet up the wall (Opposite side for the angle at the ground).
Choose the formula: Since we have Opposite and Hypotenuse, we use Sine. sin(θ) = 8 / 10 = 0.8.
Apply Inverse Sine: arcsin(0.8) ≈ 53.13°.
Find the other angle: 90° – 53.13° = 36.87°.
The Pythagorean Theorem
While this calculator focuses on angles, it also calculates the missing side length using the Pythagorean Theorem: a² + b² = c². This is essential for construction, engineering, and navigation to ensure structural integrity and correct distance measurements.
Common Applications
Using a right triangle angle calculator is vital in several real-world scenarios:
Carpentry: Calculating the pitch of a roof or the angle for stair stringers.
Navigation: Determining the course correction needed when moving between two coordinates.
Physics: Resolving force vectors into their vertical and horizontal components.
Land Surveying: Determining the height of objects or the slope of terrain.