30-60-90 Triangle

30-60-90 Triangle

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

Definition, Property

A 30-69-90 triangle is a triangle whose interior angles are 30, 60, and 90 degrees. The ratio of its sides is 1 : sqrt[3] : 2.

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

Find the value of x.

The interior angles are 90º and 30º.

So this is a 30-60-90 triangle.

Draw a 30-60-90 triangle,
whose sides are 1, √3, and 2,
next to the given right triangle.

Then these two triangles are similar.

Since these two triangles are similar,
their sides are proportional.

So 2/1 = x/√3.

Similar triangles

Solve the proportion.

Then x = 2√3.

Proportion

Example 2

Find the value of x.

The interior angles are 60º and 90º.

So this is a 30-60-90 triangle.

Draw a 30-60-90 triangle,
whose sides are 1, √3, and 2,
next to the given right triangle.

Then these two triangles are similar.

Since these two triangles are similar,
their sides are proportional.

So x/2 = 5/√3.

Multiply 2 on both sides.

Then x = (5/√3)⋅2.

5⋅ = 10

So x = 10/√3.

To remove the square root in the denominator,
multiply [√3/√3].

Then x = 10√3/3.

Rationalizing the denominator