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A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°?

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30 m

40 m

10 m

20 m

answer is A.

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Detailed Solution

Given, AC = 20 m and $∠$ C = 30°

Let, AB be the vertical pole

In $△ A B C$ ,

$\Rightarrow$ sin 30° = $\frac{A B}{A C}$

$\Rightarrow$ $\frac{1}{2}$ = $\frac{A B}{20}$ [ $∵$ sin 30° = $\frac{1}{2}$ ]

$\Rightarrow$ AB = $\frac{20}{2}$ = 10 m is our answer.

$∴$ The height of the pole is 10 m.

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