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The angle of elevation of an object from a point P on the leve

Question

The angle of elevation of an object from a point $P$ on the level ground is $α$ . Moving $d$ meters on the ground towards the object, the angle of elevation is found to be $β$ , then the height (in meters) of the object is

d tan α

d cot β

\frac{d}{cot α + cot β}

\frac{d}{cot α - cot β}

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The angle of elevation of an object from a point

P

on the level ground is

α

. Moving

d

meters on the ground towards the object, the angle of elevation is found to be

β

, then the height (in meters) of the object is

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Text solutionVerified

tan α = \frac{h}{d + a}

tan β = \frac{h}{a}

\Rightarrow tan α = \frac{h}{d + \frac{h}{tan β}}

\Rightarrow d tan α = h - h \frac{tan α}{tan β}

\Rightarrow d tan α = \frac{h ( tan β - tan α )}{tan β}

\Rightarrow h = \frac{d tan α tan β}{( tan β - tan α )}

\Rightarrow h = \frac{d}{( cot α - cot β )}

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Question Text	The angle of elevation of an object from a point $P$ on the level ground is $α$ . Moving $d$ meters on the ground towards the object, the angle of elevation is found to be $β$ , then the height (in meters) of the object is
Answer Type	Text solution:1
Upvotes	150