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 Dabca+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