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

Question

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°.

Accepted Answer

Let the height of the pole be $h$ m. The length of the rope (hypotenuse) is $20$ m. The angle of inclination is $30^\circ$. Therefore, $\sin 30^\circ = \frac{	ext{Height}}{	ext{Length of rope}} = \frac{h}{20}$. Since $\sin 30^\circ = \frac{1}{2}$, we have $\frac{1}{2} = \frac{h}{20}$, which gives $h = 10$ m.

Applications of Trigonometry

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