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Question

The angle of elevation of the top of a tower from two-point at a distance 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

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Solution

In the above figure, let AB is the tower of height h and point C and D are 4 m and 9 m respectively.

In ABC,
tanθ=ABAC
tanθ=h4(1)

Now, in ABD,
tan(90θ)=ABBD
cotθ=h9(2)

Multiply equation (1) and (2),
tanθ×cotθ=h4×h9
1=h236
h2=36
h=6 m

Hence, proved height of the tower is equal to 6 m.

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