Mathematics
The angle of elevation of the top of a tower from a point A (on the ground) is 30°. On walking 50 m towards the tower, the angle of elevation is found to be 60°. Calculate :
(i) the height of the tower (correct to one decimal place)
(ii) the distance of the tower from A.
Heights & Distances
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Answer
Consider the below figure:

(i) Let after moving 50 m towards tower from point A, the person reaches point D and height of tower be h meters.
From figure,
AD = 50 m, AB = AD + DB = (50 + DB) m
Considering right angled triangle △ABC,
Considering right angled triangle △BCD,
Putting value of h from Eq 2 in Eq 1 we get,
Hence, the height of tower is 43.3 m.
(ii) From figure,
Distance of tower from A (AB) = AD + DB = 50 + 25 = 75 m.
Hence, the distance of tower from A is 75 m.
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