Mathematics
From the top of a building 20 m high, the angle of elevation of the top of a monument is 45° and the angle of depression of its foot is 15°. Find the height of the monument.
Heights & Distances
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Answer
Let AB be the building and CD be the monument. Let length of monument (CD) be h metres.
Let distance between building and monument (BD) be x meters.
From figure,
ABDE is a rectangle so,
DE = AB = 20 meters
AE = BD = x meters
CE = CD - DE = (h - 20) meters
∠EAD = ∠ADB = 15°
Considering right angled △ABD we get,
Considering right angled △ACE we get,
Hence, the height of the monument is 94.65 meters.
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