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°. (see fig. 9.11)

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Answer 1

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Answer 2

$\large{\sf{\orange{\underline{Answer ⇢}}}}$

➠ Height of pole = 10m

$\large{\sf{\blue{\underline{step~by~step~explanation⇢}}}}$

Let AB be the vertical pole and AC be the rope.

GiveN :-

Length of rope (AC) = 20m

Angel made by the rope with the ground level (∠ACB=30) = 30°

To finD :-

Height of the pole (AB)

Solution :-

We know that sin θ = $\small{\sf{\frac{side\: opposite\:to\: θ}{hypotenuse} }}$ or $\small{\sf{\frac{AB}{AC} }}$

Hence,

Sin30° = $\large{\sf{ \frac{AB }{AC} }}$

[ As we the value of sin30° = $\frac{1}{2}$

↦$\frac{1}{2}$ = $\frac{AB}{20}$

↦AB = $\frac{1}{2} \times 20$

↦$\large{\sf{\boxed{\green{AB = 10m}}}}$

Or,

$\large{\sf{\boxed{\green{Height\:of\:pole=10m}}}}$

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