Question

From a point A that is 8.90 meters above level ground, the angle of elevation of the top of a building is 32°10' and the angle of depression of the base of the building is 14°10'. Approximate the height of the building. (Round your answer to the nearest tenth.)

Answer 1

draw a picture



find the length of the dotted line

tan(14 10) = 8.9/d

d = 8.9/tan(14 10)

the dotted line has length 35.2587 metres

now use the angle of elevation and the dotted line length to find the height y

tan (32 10) = y/35.2587

y = tan(32 10) x 35.2587

y = 22.175

the total height of the building is 22.175 + 8.9

Approx building height is 31.075 metres