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Question

The angle of elevation of the top of a vertical tower from a point on the ground is 60. From another point 10 m vertically above the first, its angle of elevation is 30 . Find the height of the tower.

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Solution

Let the height of the tower be h cm.

Now, In PAB

tan60o=APAB3=hABAB=h3(1)

And, In PCD

tan30o=PDCD13=h10CDCD=3(h10)(2)

Since, AB = CD, So, equation (2) becomes,

AB=3(h10)(3)

Equating equation (1) and (3), we get,

h3=3(h10)h=3(h10)2h=30=h=15 m

Hence, the height of the tower will be 15 m


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