Multiple choice

A circus artist is climbing from the ground along a rope stretched from the top of a vertical pole and tied to a peg at the ground. The height of the pole is 12 m and the angle made by the rope with the ground level is $30^{\circ}$ .Calculate the distance covered by the artist in climbing to the top of the pole.

  1. 12

  2. 13

  3. 24

  4. 26
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C Correct answer
Explanation

The rope forms the hypotenuse of a right triangle where the pole is the opposite side to the 30 degree angle. Using sin(30) = height / hypotenuse, we get 0.5 = 12 / hypotenuse, so the hypotenuse is 24 m.

AI explanation

The artist climbs along the rope, which acts as the hypotenuse of a right triangle where the vertical pole is the opposite side to the 30 degree angle. The trigonometric ratio for sine is opposite divided by hypotenuse, so sin 30 degrees equals 12 divided by the length of the rope. Since sin 30 degrees is 1/2, we have 1/2 equals 12 divided by the rope length, making the rope length 24 meters.

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