From a boat on the river below a dam, the angle of elevation to the top of the dam is 22°23'. if the dam is 2457 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

This illustrates a right triangle.
Given:
a(height) = 2457 ft.
∠A = 22°23' ; which is the elevation and reflects the a(height)

Find:
b(base)

Solution:

Using the law of cosine, specifically tan∠ = opposite side÷adjacent side
By analysis, tan∠A = a÷b

Since we are finding b, the formula will be derived into:
b = a÷tan∠A

Find b(base):
b = 2457 ft. ÷ tan22°23' ; substituting the numbers
b ≈ 5,966.05 ft. ; Final Answer