Question

A circus artist is climbing from the ground along a rope stretched from the top of a vertical pole and tied at the ground. The height of the pole is 12 metre and the angle made by the rope with ground level is 30°. Calculate the distance covered by the artist in climbing to the top of the pole.​

Answer 1

$\huge{\underline{\bf{Solution}}}$

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※ Clearly, distance covered by the artist is equal to the length of the rope AC.

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⟹ Let AB be the vertical pole of height 12m.

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※ It is given that ∠ACB = 30°

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★ Thus, in right - angled triangle ABC, we have

• Perpendicular AB = 12m
• ∠ACB = 30°

and we wish to find hypotenuse AC.

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$\tt:\implies\: \: \: \: \: \: \: \: {sin 30° = \dfrac{AB}{AC}}$

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$\sf\longmapsto{Since, sin30° = \dfrac{1}{2}}$

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{1}{2} = \dfrac{12}{AC}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {AC = 12 \times 2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {AC = 24m}$

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Hence, the distance covered by the Circus artist is 24m.

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