Question

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

A) 15.6 ft.
B) 21.8 ft.
C) 23.7 ft.
D) 18.4 ft.

Answer 1

The height above the ground of the base of the roof is approximately 23.7 ft.

Step-by-step explanation:

To determine the height above the ground of the base of the roof, we can use trigonometry.

Given that the ladder is 25 ft. long and the angle between the ladder and the ground is 62 degrees, we can use the sine function to find the height of the ladder.

The formula for using sine is sin(angle) = opposite/hypotenuse. In this case, the opposite side is the height of the ladder and the hypotenuse is the length of the ladder.

So, sin(62) = height/25. Rearranging the equation, we get height = 25 * sin(62). Calculating this, we find that the height of the ladder is approximately 23.7 ft.

Therefore, the base of the roof is approximately 23.7 ft above the ground.