# 45-45-90 Triangle

How to solve 45-45-90 triangle problems: definition, properties, examples, and their solutions.

## Definition, Properties

45-45-90 triangle is a triangle

whose measures of interior angles are

45º, 45º, and 90º.

It's the only isosceles right triangle.

The ratio of its sides is 1 : 1 : √2.

## Example 1

The measure of the right triangle's

non-right angle is 45º.

So this is the 45-45-90 triangle.

Then the ratio of its sides is 1 : 1 : √2.

So *x* = 7.

## Example 2

The given triangle is an isosceles right triangle.

So this is the 45-45-90 triangle.

Draw a 45-45-90 triangle next to the given triangle.

(with its sides → 1 : 1 : √2)

The given triangle is × 11 bigger.

So *x* = 11⋅√2.