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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°.

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°. NCERT Class 10 Mathematics CBSE Solutions.

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Answer

From figure,

AB is the pole.

In △BAC,

sin 30° = Side opposite to angle 30°Hypotenuse\dfrac{\text{Side opposite to angle 30°}}{\text{Hypotenuse}}

Substituting values we get :

⇒12=ABAC⇒12=AB20⇒AB=12×20=10 m.\Rightarrow \dfrac{1}{2} = \dfrac{AB}{AC} \\[1em] \Rightarrow \dfrac{1}{2} = \dfrac{AB}{20} \\[1em] \Rightarrow AB = \dfrac{1}{2} \times 20 = 10 \text{ m}.

Hence, height of pole = 10 meters.

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