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A lamp post standing at a point A on a circular path of radius

Question

A lamp post standing at a point $A$ on a circular path of radius $r$ subtends an angle $α$ at some point $B$ on the path, and $A B$ subtends an angle of $4 5^{0}$ at any other point on the path, the height of the lamp post is

2 r cot α

\frac{r}{2} tan α

2 r tan α

\frac{r}{2} cot α

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A lamp post standing at a point

A

on a circular path of radius

r

subtends an angle

α

at some point

B

on the path, and

A B

subtends an angle of

4 5^{0}

at any other point on the path, the height of the lamp post is

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Text solutionVerified

∵ A B

subtends an angle of

4 5^{o}

at any point on the circle

Therefore it subtends an angle of

9 0^{o}

at the center.

∴ A B = r^{2} + r^{2}

= r 2

tan α = \frac{h}{A B}

tan α = \frac{h}{r 2}

\Rightarrow h = r 2 tan α

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Question Text	A lamp post standing at a point $A$ on a circular path of radius $r$ subtends an angle $α$ at some point $B$ on the path, and $A B$ subtends an angle of $4 5^{0}$ at any other point on the path, the height of the lamp post is
Answer Type	Text solution:1
Upvotes	150