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Question

A tower subtends an angle α at point 'A' in the plane of its base and the angle of depression of the foot of the tower at height 'b' just above A is β. The height of the tower is

A
btanαcotβ
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B
bcotαcotβ
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C
btanαtanβ
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D
bcotαtanβ
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Solution

The correct option is A btanαcotβ
Let AP=BR=x then from ΔAPQ we find that
the height of the tower =PQ=xtanα=(bcotβ)tanα
( In triangle APB, xb=cotβ)
640540_375537_ans_eb020fb434bf4c408397c80f346d3218.png

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