Solve the problem.
-From the top of a vertical tower, 319 feet above the the surface of the earth, the angle of depression to a doghouse is 23° 3´. How far is it from the doghouse to the foot of the tower? Round your
Answer to the hundredths place when necessary.
A)749.7 ft
B)852.3 ft
C)734.11 ft
D)762.1 ft

Question

Quizplus · Accepted Answer

To solve this problem, we use the tangent of the angle of depression, which is equal to the opposite side (height of the tower) over the adjacent side (distance from the doghouse to the foot of the tower). The angle given is 23° 3´, which we convert to decimal form for ease of calculation: 23° + 3'/60 = 23.05°. The formula is tan(θ) = opposite/adjacent, so tan(23.05°) = 319/distance. Solving for distance gives us distance = 319/tan(23.05°). Using a calculator, we find that distance ≈ 749.7 feet.

Solve the Problem. -From the Top of a Vertical Tower, 319 Feet Above