Enter any two sides to find the third using the Pythagorean Theorem.
Note: For a right triangle, a² + b² = c²
function calculateTriangleSides() {
var a = document.getElementById('tri_side_a').value;
var b = document.getElementById('tri_side_b').value;
var c = document.getElementById('tri_side_c').value;
var resDiv = document.getElementById('triangle-res-area');
var resText = document.getElementById('res-text');
var valA = parseFloat(a);
var valB = parseFloat(b);
var valC = parseFloat(c);
var count = 0;
if (!isNaN(valA)) count++;
if (!isNaN(valB)) count++;
if (!isNaN(valC)) count++;
resDiv.style.display = "block";
if (count !== 2) {
resText.innerHTML = "Error: Please enter exactly TWO side lengths to calculate the third.";
return;
}
var result = 0;
var label = "";
if (isNaN(valC)) {
// Find Hypotenuse
result = Math.sqrt(Math.pow(valA, 2) + Math.pow(valB, 2));
label = "Hypotenuse (Side C)";
} else if (isNaN(valA)) {
// Find Side A
if (valC <= valB) {
resText.innerHTML = "Error: Hypotenuse must be longer than the leg.";
return;
}
result = Math.sqrt(Math.pow(valC, 2) – Math.pow(valB, 2));
label = "Side A";
} else if (isNaN(valB)) {
// Find Side B
if (valC <= valA) {
resText.innerHTML = "Error: Hypotenuse must be longer than the leg.";
return;
}
result = Math.sqrt(Math.pow(valC, 2) – Math.pow(valA, 2));
label = "Side B";
}
resText.innerHTML = "The length of " + label + " is: " + result.toFixed(4) + "";
}
function resetTriangleCalc() {
document.getElementById('tri_side_a').value = "";
document.getElementById('tri_side_b').value = "";
document.getElementById('tri_side_c').value = "";
document.getElementById('triangle-res-area').style.display = "none";
}
How to Calculate the Sides of a Triangle
Understanding how to calculate the sides of a triangle is a fundamental skill in geometry, trigonometry, and various real-world applications like construction, navigation, and engineering. The method you use depends entirely on the type of triangle you are working with and the information you already have.
1. Calculating Sides of a Right Triangle
A right triangle is a triangle where one angle is exactly 90 degrees. For these triangles, we use the Pythagorean Theorem.
Formula: a² + b² = c²
a and b: The "legs" of the triangle (the sides meeting at the 90-degree angle).
c: The "hypotenuse" (the longest side opposite the right angle).
Example: Finding the Hypotenuse
If Side A is 3 and Side B is 4, what is the length of Side C?
Square the legs: 3² = 9 and 4² = 16.
Add them together: 9 + 16 = 25.
Take the square root: √25 = 5.
The hypotenuse is 5.
2. Calculating Sides of Non-Right (Oblique) Triangles
If the triangle does not have a 90-degree angle, you cannot use the Pythagorean Theorem directly. Instead, you must use the Law of Sines or the Law of Cosines.
The Law of Cosines
Use this when you know two sides and the angle between them (SAS) or all three sides (SSS) to find an angle.
Formula: c² = a² + b² – 2ab cos(C)
Where C is the angle opposite side c.
The Law of Sines
Use this when you know two angles and one side (ASA or AAS) or two sides and an opposite angle (SSA).
Formula: a / sin(A) = b / sin(B) = c / sin(C)
3. Special Triangle Shortcuts
Certain triangles have ratios that make calculation much faster:
45-45-90 Triangle: The sides are in a ratio of 1 : 1 : √2. If the legs are length x, the hypotenuse is always x√2.
30-60-90 Triangle: The sides are in a ratio of 1 : √3 : 2. The shortest side is opposite the 30° angle, and the hypotenuse is exactly double the shortest side.
Common Questions
Can I calculate a side with only one other side?
No, you generally need at least two pieces of information (two sides, or one side and one angle) to solve for the remaining sides of a triangle.
What if the sum of two sides is not greater than the third?
According to the Triangle Inequality Theorem, the sum of any two sides must be strictly greater than the third side. If it isn't, the sides cannot form a triangle.