# Isosceles Triangle Side Calculator

Table of contents

How do I use the isosceles triangle side calculator?What is an isosceles triangle?How do I calculate the third side of an isosceles triangle?Related calculatorsFAQsWelcome 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:

**Enter the known dimensions**of your isosceles triangle. These can be its angles, height, or even a side if you know it.**Find your results**filled into their respective fields.**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.

## 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`

.

### 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.

- Calculate the cosine of
`45°`

as:

`cos(45°) = 1 / √2 = 0.7071`

- As the cosine represents the ratio of the adjacent side
`a`

to the hypotenuse`b`

, we can say that:

`cos(45°) = a / b`

- Make
`a`

the subject and complete the equation:

`a = b × cos(45°) = 14.14 cm`