In a 30°- 60°- 90° triangle, the length of the hypotenuse is 30. Find the length of the shorter leg?

Solution:

Given, the length of the hypotenuse is 30.

Let the side opposite 30° be the shortest side.

The side opposite 60° is the longest side.

So, the side opposite to 90° is the hypotenuse.

We know that the ratio of the sides of a 30-60-90-triangle is 1: √3 :2

Length of the shortest side is x.

The length of longest side is √3(x)

The length of the hypotenuse is 2x.

We know, 2x = 30

Length of the shortest side, x = 15

Therefore, the length of the shorter leg is 15 units.

In a 30°- 60°- 90° triangle, the length of the hypotenuse is 30. Find the length of the shorter leg?

Summary:

In a 30°- 60°- 90° triangle, the length of the hypotenuse is 30. The length of the shorter leg is 15 units.