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A circus artist climbs on a rope which is tied between the top of a pole and a fixed point on the level ground. The height of the pole is 12 m and the rope makes an angle of with the ground. What will be the distance covered by the artist to climb to the top of the pole while taking $sin θ = 0.5783$ ?

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20.75m

20m

20.30m

21m

answer is A.

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Detailed Solution

Given that,
The height of the pole = 12m
The rope makes an angle=

θ

The value of

sin θ = 0.5783

We construct the diagram,
Question Image

Considering,
the height of the pole AB=12 m
the length of rope = AC
the distance between the rope and foot of the pole = BC.
Substituting the values of

sin θ = 0.5783

, AC and AB in

sin θ = h e i g h t h y p o t e n u s e

⇒ sin θ = A B A C ⇒ 0.5783 = 12 A C ⇒ A C = 12 0.5783 ⇒ A C = 20.75 m

Thus the length of the rope will be

m.
Therefore the correct option is 1.

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