From a point A that is 050 meters above level ground the ang

From a point A that is 0.50 meters above level ground, the angle of elevation of a building is 32 and the angle of depression of the base of the building is 16 degree. Approximate the height of the building. Enter an exact answer or round your answer to the nearest tenth. (To present an angle in degrees, type dog or use the Clasped symbol. For example, sin(30dag)) m

Solution

1. Calculate length of side BC (x) of triangle DBC.

2. Using our answer for length of side BC (x), calculate length of side AB (h, height of building) of triangle ABC.

tan(16°) = 0.5/x

0.28674 = 0.5/x

0.28674x = 0.5

x = 0.5/0.28674

x = 0.14337 m (length of side BC)

Our calculation for length of side AB (h, height of building):

90º - 32º = 58°

  tan 57º= x/h

1.6033 = 0.14337/h

1.60033h = 0.14337

h = 0.08 m (height of building)