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Question

The angle of elevation of top of tower from a point A due south of the tower is α and from a point B due East of the tower isβ. If AB = d, then the height of tower is 


Your Answer
A
dtan2αtan2β
Your Answer
B
dtan2α+tan2β
Correct Answer
C
dcot2α+cot2β
Your Answer
D
dcot2αcot2β

Solution

The correct option is C dcot2α+cot2β


OB=h cot βandOA=h cotα
Then OB2+OA2=h2 cot2β+h2 cot2αd2=h2(cot2α+cot2β)h2=d2cot2α+cot2βh=dcot2α+cot2β

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