Question

A landscaper is making a retaining wall to shore up the side of a hill. To ensure against collapse, the wall should make an angle 75° with the ground.

If the wall is 25 feet, what is the height of the hill?
Question options:

25.9 ft

6.5 ft

24.1 ft

93.3 ft

Answer 1

C. 24.1 ft

Explanation:

The side of the wall making the tilt of 75° will represent the hypotenuse

The height of the wall will be represented by the side opposite to the angle 75°

Apply the relationship for sine of angle Ф

Formula to use is ;

Sin Ф= length of opposite side÷hypotenuse

SinФ=O/H

Sin 75°=O/25

0.96592582628=O/25

O=0.96592582628×25 =24.1 ft