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Question

The angle of elevation of the top of a hill from a point is α. After walking b meters towards the top up a slope inclined at an angle β to the horizontal, the angle of elevation of the top becomes γ. Then the height of the hill is

A
bsinαsin(γβ)sin(γβ)
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B
bsinαsin(γα)sin(γβ)
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C
bsin(γα)sin(γβ)
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D
bsin(γβ)sin(γα)
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Solution

The correct option is A bsinαsin(γβ)sin(γβ)
Let BC be the hill and C be the top of hill.
CAB=α
PA=b
From right angle PAD
sinβ=a2ba2=bsinβ.....(1)
also from CQP,a1=PCsinγ....(2)
PCA=γα
bsin(γa)=PCsin(αβ)PC=bsin(αβ)sin(γa)
from (2)
a1=bsin(αβ)sinγsin(γa)...(3)
Height of hill =bsin(γa)[sinβsin(γa)+sin(αβ)sin(γa)sinγ]
=bsinαsin(γa)[sinγcosβsinβcosγ]=bsinαsin(γβ)sin(γβ)
734577_692810_ans_4ec3e151d5eb4176b76f246fc88dec40.png

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