Question

A 16-foot ladder leans against a wall so that the ladder’s angle of elevation is 55°. Find x, the distance between the foot of the ladder and the base of the building. Use cosine to solve for the missing side and round your answer to the nearest hundredth.(1 point) Responses x=13.11 ft. x equals 13.11 ft. x=9.18 ft. x equals 9.18 ft. x=27.90 ft. x equals 27.90 ft. x=52.87 ft. x equals 52.87 ft.

Answer 1

To find the distance x between the foot of the ladder and the base of the building, we can use the cosine function.

cos(55°) = adjacent/hypotenuse

Let x be the adjacent side and 16 feet be the hypotenuse:

cos(55°) = x/16

Solving for x:

x = 16 * cos(55°) ≈ 16 * 0.5736 ≈ 9.18 ft

Therefore, the correct answer is x = 9.18 ft.