Question

A 16-foot ladder leans against a wall so that the ladder’s angle of elevation is $55^{\circ}$. 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.Answer Choices$x = 13.11\text{ ft.}$$x = 27.90\text{ ft.}$$x = 52.87\text{ ft.}$$x = 9.18\text{ ft.}$

Answer 1

Cosine relates the adjacent side x to the hypotenuse 16:
cos 55° = x / 16
So x = 16 cos 55° ≈ 16(0.573576) ≈ 9.18 ft.

Answer: x = 9.18 ft.