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JEE Main 2007

Exam: JEE Main
Year: 2007
Subject: Mathematics
Chapter: Heights and Distances

JEE Main 2007 · Mathematics · Heights and Distances

A tower stands at the centre of a circular park. A and B are two...

A tower stands at the centre of a circular park.

A

and

B

are two points on the boundary of the park such that

A B(=a)

subtends an angle of

60^{\circ}

at the foot of the tower, and the angle of elevation of the top of the tower from

A

or

B

is

30^{\circ}

. The height of the tower is A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that A B(=a)

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that A B(=a)

Options

A $\frac{2 a}{\sqrt{3}}$
B $2 a \sqrt{3}$
C $\frac{a}{\sqrt{3}}$
D $a \sqrt{3}$

Correct answer

C. $\frac{a}{\sqrt{3}}$

Step-by-step solution

\triangle

\mathrm{O A B}

is equilateral

\therefore

\mathrm{OA}=

\mathrm{OB}=\mathrm{AB}

=

\mathrm{a}

Now

\tan 30^{\circ}=\frac{h}{a} \therefore h=\frac{a}{\sqrt{3}}

\text{. }

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