Question

A ladder leans against a side of a building, making a 63-degree angle with the ground, and reaching over a fence that is 6 feet from the building. The ladder barely touches the top of the fence, which is 8 feet tall. Find the length of the ladder.

Answer 1

22.19 feet

Explanation:

You want the length of a ladder that makes a 63° angle with the ground and reaches over an 8 ft fence to a building 6 ft beyond.

Trig functions

The relevant trig relations are ...

Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin

Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos

Application

Using these relations, we can find the lengths of the segments of the ladder between the ground and the fence, and between the fence and the building.

Referring to the attached diagram, we have ...

CE = 8/sin(63°) ≈ 8.9786

FC = 6/cos(63°) ≈ 13.2161

Then the total length of the ladder is ...

FE = CE +FC

FE = 8.9786 +13.2161 = 22.1947

The length of the ladder is about 22.19 feet.