The angles of elevation of the top of a tower from two points at distances of 5 metres and 20 metres from the base of the tower and in the same straight line with it, are complementary. Find the height of the tower.
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The angles of elevation of the top of a tower from two points at distances of 5 metres and 20 metres from the base of the tower and in the same straight line with it, are complementary. Find the height of the tower.
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Answer:
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Step-by-step explanation:
THE DIAGRAM IS IN THE ABOVE PICTURE
From figure: Let θ be the angle of elevation.
Given: Angle are complementary, so another angle is (90- θ)°
From right triangle CAB: tan θ = AB/AC tan θ = h/5 or h = 5tan θ ….(1)
Form another right triangle DAB:
tan (90-θ)° = AB/AD tan (90-θ)° = h/20 or h = 20 tan (90-θ)° or h = 20 cot θ …(2)
Multiply equation (1) and (2), we get h2 = 100 x tan θ x cot θ h = 10 (As tan θ = 1/cotθ)
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