Question

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 29º. 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?

x (x)

Answer 1

şo) According to the question, the height of the mountain is observed from two points and the angles of elevation 29° and 33: The distance between the points is dooo feet. The situation is shown in the diaglam below. were A # 29 33 Сх D Zooft In the DABC Tan33 - Height base AB CB tan 33 = H х H : x tap 33 In the D ABD tan29= Height AB Base OB tan at AB o't+CB H tana9° 2000 + x H = (22000 + x) tan 29

Equaiting the heignt # (2000 + x)tan 29 x tan 33 so olan 2 + xton 2 xa 33 xltan 33 - tan 29) 2000 tan 29° 2000 fan 29 0.6h 94-0.5.543 2000 x (0.5543) 0.6494-0.5543 x = 1108.6 0.0951 X = , so X using the value of in the equation H = x tan33 #= (11,657.2)x(tan 33) • 7,570.3 H = 7570.27 :: The height of the building is approximately" 7,5 70 feet