Question

From a boat on the lake, the angle of elevation to the top of a cliff is 27°57'. If the base of the cliff is 128 feet from the boat, how high is the cliff (to the nearest foot)?

Answer 1

Height of cliff = 67.92 ft

Explanation:

Refer the figure given

Distance to base of cliff from boat = AB = 128 feet

Angle of elevation to the top of a cliff = ∠ABC = 27°57'

We need to find height of cliff = AC

We have

`tan(27^057')=(AC)/(AB)=(AC)/(128)\\\\AC=67.92ft`

Height of cliff = 67.92 ft

Answer 2

If the base of the cliff is 128 feet from the boat, the cliff is 68 feet high. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.