Question

A 35-foot tall pole is leading towards a building. To stop the pole from leaning

further, a 48-foot long cable is secured from the top of the pole to a stake in the
ground opposite of the building. If the stake is 30 feet from the pole, what angle
does the cable make with the pole?

Answer 1

9514 1404 393

Answer:

38.5°

Explanation:

You are given all three side lengths of the relevant triangle, so the Law of Cosines can be used to find any desired angle. If we call the desired angle C, then that law tells you ...

C = arccos((a² +b² -c²)/(2ab))

where a and b are the triangle side lengths adjacent to the angle of interest, and c is the side opposite. Here, 'a' and 'b' are the pole and cable lengths, and 'c' is the distance of the stake from the pole.

C = arccos((35² +48² -30²)/(2·35·48)) = arccos(2629/3360)

C ≈ 38.515°

The cable makes an angle of about 38.5° with the pole.