Question

A 25 ft. ladder is leaning against the roof of a house. The angle between the ladder and the ground is 62°. How high above the ground is the base of the roof?

a) (12.5) ft
b) (15.5) ft
c) (20.5) ft
d) (22.5) ft

Answer 1

The height of the base of the roof is approximately 22.5 ft above the ground.

Step-by-step explanation:

To find the height above the ground of the base of the roof, we can use trigonometry. The ladder forms a right triangle with the ground and the side of the house. We know the length of the ladder (25 ft.) and the angle between the ladder and the ground (62°). We can use the sine function to find the height:

Sin(62°) = height / 25 ft.

Height = Sin(62°) x 25 ft.

Height ≈ 22.5 ft.

Therefore, the base of the roof is approximately 22.5 ft above the ground.