Question

A ladder is leaning against a building forming an 65° angle with the ground. The length of the ladder is 9 ft. How far is the base of the ladder from the base of the building? Round your answer to the nearest tenth.

Answer 1

3.8 feet

Explanation:

You want to know the distance from a building to the base of a 9 ft ladder that makes a 65° angle with the ground.

Cosine

The cosine relation is ...

Cos = Adjacent/Hypotenuse

In the right triangle that models this geometry, the hypotenuse is the length of the ladder (9 ft), and the distance from the base of the ladder to the base of the building is the side adjacent to the 65° angle.

Solving the above relation for the adjacent side, we have ...

Adjacent = Hypotenuse · Cos

distance to building = (9 ft)·cos(65°) ≈ 3.8 ft

The base of the ladder is about 3.8 ft from the base of the building.