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

Solution:

We know that in a 30-60-90 triangle, we have the sides in the ratio 1 :√3 : 2

Given, the length of the hypotenuse is 30.

Let the side opposite to 30° be the shortest side.

The side opposite to 60° is the longest side.

So, the side opposite to 90° is hypotenuse.

Length of the shortest side is x.

Length of longest side is √3(x)

Length of the hypotenuse is 2x.

We know, 2x = 30

x = 15

By Pythagoras theorem,

x² + (√3x)² = (2x)²

(15)² + (√3x)² = (30)²

(√3x)² = (30)² - (15)²

(√3x)² = 900 - 225

Longest side = √675

= 15√3

Use √3 = 1.732

Longest side = 15(1.732)

= 25.98 units.

Therefore, the length of the longer leg is 25.98 units.

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

Summary:

In a 30°-60°-90° triangle, the length of the hypotenuse is 30. The length of the longer leg is 25.98 units.