for a man the angle of elevation for the highest point of a temple situated east of him is 60° on walking 240 metres to North the angle of elevation changes to 30 degrees then the height of the temple is
Answers
The height of the temple is 146.97 m (60√6 m)
Step-by-step explanation:
for a man the angle of elevation for the highest point of a temple situated east of him is 60°
Let say height of temple = h m
=> Tan 60° = Height of temple /Distance of temple in East
=> √3 = h/Distance of temple in East
=> Distance of temple in East = h/√3 m
Man walks 240 m in North
Man Distance from base of temple = √((h/√3)² + 240²)
= √(h²/3 + 57600)
= √((h² + 172800)/3)
angle of elevation changes to 30°
Tan 30° = h/ √((h² + 172800)/3)
=> 1/√3 = h/ √((h² + 172800)/3)
=> √(h² + 172800) = 3h
Squaring both sides
=> h² + 172800 = 9h²
=>8h² = 172800
=> h² = 21600
=> h = 60√6
=> h = 146.97 m
the height of the temple is 146.97 m
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