30-60-90 Triangle

How to find the sides of the given 30-60-90 triangle: definition, 2 examples, and their solutions.

Formula

Formula

A 30-60-90 triangle is a triangle
whose interior angles are 30º, 60º, and 90º.

The ratio of its sides is
1 : √3 : 2.

Example 1

Example

Solution

The given interior angles of the triangle are
90º and 30º.

So this triangle is a 30-60-90 triangle.

So draw a 30-60-90 triangle
whose sides are 1, √3, and 2.

These two triangles are similar.

Then their sides are proportional.

So x/√3 = 2/1.

Similar Triangles

2/1 = 2

x/√3 = 2

Multiply √3 to both sides.

Then x = 2√3.

So x = 2√3.

Example 2

Example

Solution

The given interior angles of the triangle are
60º and 90º.

So this triangle is a 30-60-90 triangle.

So draw a 30-60-90 triangle
whose sides are 1, √3, and 2.

These two triangles are similar.

Then their sides are proportional.

So x/2 = 5/√3.

Multiply 2 to both sides.

Then x = 10/√3.

Rationalize the denominator3
by multiplying √3/√3.

Then x = 10√3/3.

So x = 10√3/3.