# 30-60-90 Triangle

See how to solve a 30-60-90 triangle.

2 examples and their solutions.

## 30-60-90 Triangle

### Definition, Property

whose interior angles are 30º, 60º, and 90º.

The ratio of the sides is

1 : √3 : 2.

### Example

x√3 = 21 - [2]

x√3 = 2

x = 2√3

[1]

Interior angles: 30°, 90°

→ This is a 30-60-90 triangle.

→ Draw a (1, √3, 2) triangle.

→ This is a 30-60-90 triangle.

→ Draw a (1, √3, 2) triangle.

[2]

These two triangles are similar.

So set a proportion by using the corresponding sides.

So set a proportion by using the corresponding sides.

Close

### Example

x2 = 5√3

x = 2⋅5√3⋅√3√3 - [2]

= 10√33

[1]

Interior angles: 60°, 90°

→ This is a 30-60-90 triangle.

→ Draw a (1, √3, 2) triangle.

→ This is a 30-60-90 triangle.

→ Draw a (1, √3, 2) triangle.

Close