Q. 204.0( 10 Votes )

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 is
A.

B.

C.

D.

Answer :

Untitled23.jpg


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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