The angles of depression of the top and bottom of a building 50 metres high as observed from the top of a tower are 30° and 60° respectively .Find the height of the tower and the horizontal distance between the building and the tower.
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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
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