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Question

From the top of a cliff of height a, the angle of depression of the foot of a certain tower is found to be double the angle of elevation of the top of the tower of height h. If θ be the angle of elevation then its value is:

A
cos12ha
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B
sin12ha
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C
sin1a2h
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D
tan132ha
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Solution

The correct option is D tan132ha
h - a = x tan θ
a = x tan 2θ
(h - a)/a = tanθtan2θ=1tan2θ2
(h/a) - 1 = 1tan2θ2
(h/a) - 1 - 1/2 = tan2θ2
tan2θ = 3 - (2h/a)
tan θ = 3(2h/a)
θ = tan132ha
1048011_1006571_ans_375d54171ff044b09ba0b30f4f2dbfb9.bmp

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