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Question

The angles of elevation of the top of a tower from two points at a distance of 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.
466375_64a7b3c35df141a081674baec4c1b5f7.png

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Solution


C and D are complementary .....given

In ABC,ABBC=tanQ ...(i)

In ABD,ABBD=tan(90Q)

AB9=cotQ ...(ii)

AB9=1tanQandtanQ=7AB

Put value of tanQ in eqn (ii)

ABBC=9AB

AB2=9BC

AB=36=6

Height of tower =6m

494931_466375_ans_39177f99d1e04449a8ce6028f78c6e3a.png

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