# Isosceles Triangle Side Calculator

Created by Rijk de Wet
Reviewed by Steven Wooding
Last updated: May 31, 2022

Welcome to the isosceles triangle side calculator, where we'll learn all there is to know about an isosceles triangle's sides. In this article, we explain:

• What an isosceles triangle is;
• How to calculate the third side of an isosceles triangle; and
• How to calculate the sides of an isosceles right triangle from the hypotenuse.

## How do I use the isosceles triangle side calculator?

Using the isosceles triangle side calculator is as easy as counting to three! All you need to do is:

1. Enter the known dimensions of your isosceles triangle. These can be its angles, height, or even a side if you know it.
2. Find your results filled into their respective fields.
3. The calculator can work backward, too: fill in the sides, and the calculator will work out all the other dimensions.

If you'd like to learn how the side lengths are calculated, read on!

## What is an isosceles triangle?

An isosceles triangle is a triangle with two equally long sides (which we call the legs) and are both denoted with a. The remaining side is denoted by b and is unique. The angles adjacent to b (which we call the base angles α) are also equal due to the legs being equal in length. The remaining angle at the top is called the vertex angle β and is unique. An isosceles triangle. Note that the legs marked a are the same length, and the corners marked α are the same angle.

## How do I calculate the third side of an isosceles triangle?

If the only unknown side is the base side b, our steps depend on what information we have. Usually, we have the leg length a, the base angle α, and the vertex angle β. We can then apply trigonometry to one half of the isosceles triangle, which is a right triangle with angles α and β/2, a hypotenuse of length a, and a side of length b/2. From there, we can calculate b/2 and then b.

If you found that this isosceles triangle side calculator isn't acute enough, might we interest you in some of our other isosceles triangle calculators?

## FAQ

### How do I calculate the sides of an isosceles right triangle from its hypotenuse?

An isosceles right triangle has a vertex angle of β = 90° and base angle α = 45°. We can use trigonometry to calculate the remaining side because it's a right triangle, and we know its angles. We want to calculate the side length a, and we have the hypotenuse b. So, we can easily say that a = b × cos(45°).

### What is the length of the equal sides of an isosceles right triangle with hypotenuse 20 cm?

Because we know an isosceles right triangle's angles to be 45°, 45°, and 90°, we can work out the equal side lengths a with trigonometry.

1. Calculate the cosine of 45° as:
cos(45°) = 1 / √2 = 0.7071
2. As the cosine represents the ratio of the adjacent side a to the hypotenuse b, we can say that:
cos(45°) = a / b
3. Make a the subject and complete the equation:
a = b × cos(45°) = 14.14 cm
Rijk de Wet Vertex angle (β)
deg
Base angle (α)
deg
Height from apex (hb)
in
Area
in²
Perimeter
in
Sides
Leg (a)
in
Base (b)
in
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