Question

An engineer designs a 65-foot cellular telephone tower. Find the angle of elevation to the top of the tower at a point on level ground 40 feet from its base. (Round your answer to one decimal place.)

Answer 1

the angle of elevation is 58.4°

Explanation:

Given the data in the question and as illustrated in the image below;

let ∅ be the angle of elevation;

Opposite (AC) = 65 ft

Adjacent (CB) = 40 ft

we know that; from SOH CAH TOA

TOA

tan∅ = Opposite / Adjacent

so;

tan∅ = 65 / 40

tan∅ = 1.625

∅ = tan⁻¹ ( 1.625 )

∅ = 58.3924 ≈ 58.4°

Therefore, the angle of elevation is 58.4°