# 30-60-90 Triangle

How to solve 30-60-90 triangle problems: definition, property, examples, and their solutions.

## Definition, Property

30-60-90 triangle is a triangle

whose measures of interior angles are

30º, 60º, and 90º.

The ratio of its sides is 1 : √3 : 2.

## Example 1

The measure of the right triangle's

non-right angle is 30º.

So this is the 30-60-90 triangle.

Draw a 30-60-90 triangle next to the given triangle.

(with its sides → 1 : √3: 2)

The given triangle is × 2 bigger.

So *x* = 2⋅√3.

## Example 2

The measure of the right triangle's

non-right angle is 30º.

So this is the 30-60-90 triangle.

Draw a 30-60-90 triangle next to the given triangle.

(with its sides → 1 : √3: 2)

It's hard to find the scale factor.

But these two triangles are similar.

So set a proportion between the triangles:*x* / 2 = 5 / √3.

Similarity of sides in triangles