Mathematics
A man observes the angle of elevation of the top of a building to be 30°. He walks towards it in a horizontal line through its base. On covering 60 m, the angle of elevation changes to 60°. Find the height of the building correct to the nearest metre.
Heights & Distances
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Answer
Let QR be the tower and man be initially at point P after moving 60 m let it reach point S.
PS = 60 m
From figure,
PQ = PS + SQ = (SQ + 60) m. (Eq 1)
Considering right angled △SQR, we get
Considering right angled △PQR, we get
Putting value of QR from Eq 2, in Eq 3 we get,
From Eq 2,
Correcting upto nearest meter QR = 52.
Hence, the height of building is 52 meters.
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