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