A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 30 ∘ . From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 33 ∘ . How high (in feet) is the mountain?
Accepted Solution
A:
Answer:10406.5937 ftStep-by-step explanation:In the figure attached the graph of the problem is shown.Data for triangle ABC:∠A = 30°∠B = 180° - 33° = 147°, segment AB = 2000 feet long. ∠C = 180° - 30° - 147° = 3° From law of sines:AB/sin(C) = AC/sin(B)2000/sin(3) = AC/sin(147)AC = [2000/sin(3)]*sin(147)AC = 20813.1875 ftUsing now triangle ADC:sin(A) = CD/ACCD = sin(A)*ACCD = sin(30)*20813.1875CD = 10406.5937 ft