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Question

Two posts are x meters apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in meters) of the shorter post is,

A
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B
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C
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D
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Solution

The correct option is C

Above figure is the representation of the given question
We have to find h in terms of x
tanθ=h(x2)=2hx....(i)
tan(90θ)=cotθ=2h(x2)=4hx....(ii)
Multiplying (i) and (ii),
tanθ×cotθ=(2hx)×(4hx)
1=8h2x2
h=x22

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