The angle of elevation of the top of a hill from a point is α. After walking b towards the top up of a slope inclined at an angle β to the horizon, the angle of elevation of the top becomes γ. Then the height of hill is
A
bsinαsin(γ−β)sin(γ−α)
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B
bsinαsin(γ−α)sin(γ−β)
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C
bsin(γ−β)sin(γ−α)
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D
sin(γ−β)bsinαsin(γ−α)
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Solution
The correct option is Absinαsin(γ−β)sin(γ−α) h=x+bsinβ=(hcotα−bcosβ)tanγ+bsinβ⇒h(1−cotαtanγ)=bsinβ−bcosβtanγ⇒h=b(sinβ−cosβtanγ)(1−cotαtanγ)=bsinαsin(γ−β)sin(γ−α)