The angle of elevation of the top of a hill from a point is - After walking b towards the top up of a slope inclined at an angle - to the horizon- the angle of elevation of the top becomes Y- Then the height of hill isA- nor sin y -B- sin 1-1- b sin-sin y -C- sin -D- b sin-sin -sin -

The correct option is D b sin α sin (γ β)/sin(γ α) h = x + bsin β = (hcot α b cos β)tan γ + bsin β ⇒ h(1 cot α tan γ) = b sin β b cos β tan γ ⇒ h = ...

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Standard XII

Mathematics

Angle between Two Lines

The angle of ...

Question

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

\frac{b s i n α s i n (γ - β)}{s i n (γ - α)}

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\frac{b s i n α s i n (γ - α)}{s i n (γ - β)}

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\frac{b s i n (γ - β)}{s i n (γ - α)}

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\frac{s i n (γ - β)}{b s i n α s i n (γ - α)}

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Solution

The correct option is A $\frac{b s i n α s i n (γ - β)}{s i n (γ - α)}$

$h = x + b s i n β = (h c o t α - b c o s β) t a n γ + b s i n β \Rightarrow h (1 - c o t α t a n γ) = b s i n β - b c o s β t a n γ \Rightarrow h = \frac{b (s i n β - c o s β t a n γ)}{(1 - c o t α t a n γ)} = \frac{b s i n α s i n (γ - β)}{s i n (γ - α)}$

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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

The correct option is A b sinα sin(γ−β)sin(γ−α) h=x+bsinβ=(hcotα−bcosβ)tanγ+bsinβ⇒h(1−cotα tanγ)=b sinβ−b cosβ tanγ⇒h=b(sin β−cosβ tanγ)(1−cotα tanγ)=b sinαsin(γ−β)sin(γ−α)

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