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Question

A vertical pole PS has two marks at Qand A such that the portions PQ, PR and PS subtend angles α,β,γ at a point on the ground distant x from the pole. If PQ = a, PR -b, PS = c and α+β+γ = 180; then x2 =

A
aa+b+c
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B
ba+b+c
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C
ca+b+c
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D
abca+b+c
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Solution

The correct option is D abca+b+c
PQ = a = x tan α, PR = b = x tan β
PS = c = tab γ
a + b + c = x ( tan α + tan β + tan γ)
abc = x3.tan α.tan β. tan γ
Dividing abc/a + b +c = x2.1 (d)
when α + β + γ = 1800 then
tan α + tan β + tan γ = tan α.tan β. tan γ
i.e. S1=S3
1083719_1006531_ans_6b46a971d86143df80b6c149a425aabc.JPG

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