# Isosceles Triangle Height Calculator

This isosceles triangle height calculator will calculate for you the two heights of an isosceles triangle. It will also tell you whether you have a valid isosceles triangle. Read on to learn about:

- What is an isosceles triangle?
- How to calculate the height of an isosceles triangle.
- The isosceles triangle height formula.

## What is an isosceles triangle?

An isosceles triangle is a triangle where **two sides are of equal length**. You can also argue that a triangle where all three sides are equal (an equilateral triangle) is a special case of an isosceles triangle.

Isosceles triangles date back to ancient Egypt, where it was used for decoration and in their architecture — even the face of a pyramid is an isosceles triangle.

## Isosceles triangle height formula

We can derive the formula for the height of an isosceles triangle (as measured from the base to the vertex between the two equal legs) from **Pythagoras's Theorem** if we look for a right-angle triangle inside the isosceles triangle.

You can form one if you only consider half of an isosceles triangle, cutting at the midpoint of the base (side $b$ in the figure above the calculator). Then we can derive the height $h$ starting from Pythagoras's equation:

## How to use the isosceles triangle height calculator

Using this isosceles triangle height calculator is really straightforward. Here are the steps to follow:

- Enter a value for the
**length of each leg**of the triangle (the two equal sides). - Input the length of the
**base**of your isosceles triangle. - You'll instantly receive a value for the
**height of the triangle**, as measured from the base to the vertex (h_{b}). - As a bonus, you'll also get the height as measured from the leg side to the opposite vertex at the end of the base (h
_{a}).

Note that if you want to calculate the lengths in different units, you can change the unit before entering a value. Changing the unit after entering a value, the calculator is also a length unit converter.

## Other isosceles triangle calculators

Here are some other isosceles triangle calculators that you might be interested in:

## FAQ

### How do I find the height of an isosceles triangle?

To find the height of an isosceles triangle, follow these steps:

**Square**the length of the two equal sides.**Square**the unequal side length,**divide**by four, and**subtract**the result from Step 1.- Take the
**square root**of the result from Step 2. - The result is the height of an isosceles triangle.

### What is the height of an isosceles triangle with a base of 10 cm and a leg of 15 cm?

**14.1 cm**. To arrive at this answer, the following formula for the height of an isosceles triangle was used:

**h = √[a² − (b²/4)]**

Plugging in the numbers:

**h = √[15² − (10²/4)] = √200 = 14.1 cm**