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A kite flying at a height of 75 m from the ground is attached to a straight string which is inclined at an angle of 60 $°$ to the ground. The length of the string is

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75 m

50 \sqrt{3} m

50 m

75 \sqrt{3} m

answer is B.

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Detailed Solution

It is given that a kite flying at a height of 75 m from the ground which is attached to a straight string inclined at an angle of

60 °

to the ground.
According to the given data the figure has been drawn below.
Question Image

ΔABC

let AB represents the height of the kite and the length of the string is h m.
The inclined angle is

∠ ACB = 60 °

.
Here in

ΔABC

, we get,

sin θ = P e r p e n d i c u l a r H y p o t e n u s e

\sin 60 ° = \frac{AB}{AC}

\Rightarrow \sin 60 ° = \frac{75}{h}

\Rightarrow h = \frac{75}{\sin 60 °}

\Rightarrow h = \frac{75}{\frac{\sqrt{3}}{2}}

∵ sin 60 ° = 32

\Rightarrow h = \frac{75 \times 2}{\sqrt{3}}

\Rightarrow h = 50 \sqrt{3}

So the length of the string is

50 \sqrt{3} m

.
So, the correct option is 2.

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