If the angles of elevation of the top of a tower from two points at distances a and b from the base and in the same straight line with it are complementary then the height of the tower isA. B. C. D.

In the above figure, let AB be the tower and C and D be the two points on the ground from where A is observed. Join B, C, D. Let BC = a and BD = b. Join C, D with A. We get two right-angled triangles ABC and ABD with right angle at B. Also, the angles of elevation of the top of the tower AB from C and D are ACB and ADB respectively. These angles are complementary. So, We are to find the height of the tower, that is, AB.

From ∆ABD,

Again, from ∆ABC,

or,

or,

Now, multiplying we get,

or,

or,

AB = √ab

So the correct choice is (B).

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