Trignometry applications

Level pending

Anand is watching a circus artist climbing a 20m long rope which is tightly stretched and tied from the top of vertical pole to ground . Find the height of the pole it the angle made by the rope with the ground level is 30.

Answer must be in metre so only number


The answer is 10.

Nischal Kumar by Nischal Kumar , 22, India

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1 solution

Caleb Townsend
Feb 21, 2015

The ground, pole, and rope form a right triangle. The definition of sin ⁡ \sin is sin ⁡ θ ≡ opposite hypotenuse \sin\theta \equiv \frac{\text{opposite}}{\text{hypotenuse}} In this case, the rope is the hypotenuse and the height of the pole is the opposite side. Therefore h = r × sin ⁡ θ = 20 sin ⁡ 3 0 ∘ = 10 h = r\times\sin\theta = 20 \sin30^\circ = \boxed{10}

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