Solve the problem.
-From a distance of 43 feet from the base of a building, the angle of elevation to the top of the building is 67°. Estimate the height of the building to the nearest foot.
A) 101 feet
B) 40 feet
C) 18 feet
D) 17 feet

Question

Quizplus · Accepted Answer

To find the height of the building, we can use the tangent of the angle of elevation, which is the ratio of the opposite side (height of the building) to the adjacent side (distance from the building). The formula is tan(θ) = opposite/adjacent. Here, θ = 67° and the adjacent side = 43 feet. Rearranging the formula gives us the height = tan(67°) * 43. Using a calculator, tan(67°) ≈ 2.35585, so the height ≈ 2.35585 * 43 ≈ 101.30155 feet. Rounding to the nearest foot gives us approximately 101 feet.

Solve the Problem. -From a Distance of 43 Feet from the Base of the Base