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Question

A flagstaff stands vertically on a pillar,the height of the flagstaff being double the height of the pillar. A man on the ground at a distance finds that both the pillar and the flagstaff subtend equal angles at his eyes. The ratio of the height of the pillar and the distance of the man from pillar, is

A
3:1
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B
1:3
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C
1:3
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D
3:2
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Solution

The correct option is C 1:3

Let AB be the height of flagstaff and BC be the height of pillor.
AB=2hξBC=h
Now, in ADC
tan2θ=ACCD=3hx
tan2θ=3hx(1)
In tanθ=hx(2)
From (1),
tan2θ=3hx
2tanθ1tan2θ=3hx
Using equation (2),
2(hx)1(hx)2=3hx
2=3[1(hx)2]
2=33(hx)2
3(hx)2=1
(hx)2=13
hx=13
h:x=1:3
Hence, the answer is 1:3.



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