Question

The angles of depression of the top and bottom of a building 50 meters
high as observed from the top of a tower are 30˚ and 60˚ respectively.
Find the height of the tower, and also the horizontal distance between the
building and the tower.​

Answer 1

Answer:

In ΔBTP,

tan 30° = TP/BP

1/√3 = TP/BP

BP = TP√3

In ΔGTR,

tan 60° = TR/GR

√3 = TR/GR

GR = TR/√3

As BP = GR

TP√3 = TR/√3

3 TP = TP + PR

2 TP = BG

TP = 50/2 m = 25 m

Now, TR = TP + PR

TR = (25 + 50) m

Height of tower = TR = 75 m

Distance between building and tower = GR = TR/√3

GR = 75/√3 m = 25√3 m