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Question

A man standing on a level plane observes the elevation of the top of a pole to be θ. If he walks a distance equal to double the height of the pole towards the pole, the angle of elevation becomes 2θ. Then the value of θ (in degrees) is

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Solution


Let AB be the pole with height h.
In ABC
x=hcot2θ (i)
In ABD
h=(2h+x)tanθ (ii)

From equation (i) and (ii),
h=(2h+hcot2θ)tanθ1=(2+cot2θ)tanθ (h0)1=(2+1tan2θ)tanθ1=(2+1tan2θ2tanθ)tanθtan2θ4tanθ+1=0tanθ=4±122tanθ=2+3,23θ=75,15
As 2θ is an acute angle, so
θ=15

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