Question

Two buildings mounted vertically on a level ground are 18 m apart. From the top of the short building the top of the other building can seen at an angle of elevation 45º and bottom can be seen at an angle of depression 30º. Find the height of the buildings​

Answer 1

Answer:

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Step-by-step explanation:

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