Question

1. 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°

Answer 1

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Refer The Attachment ✌

Answer 2

Given:

• Length of the rope is 20 m
• Angle with the ground level is 30°
• AC = 20 m
• ${\tt{ \angle C = 30° }}$

To Find:

• Height of the pole

Solution

Let AB be the vertical pole

In right ΔABC,

Using sin formula;

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

:: Value of sin 30° is ½,

$\colon\implies{\tt{ \dfrac{1}{2} = \dfrac{AB}{20} }} \\ \\ \\ \colon\implies{\tt{2AB = 20 }} \\ \\ \\ \colon\implies{\tt{AB = \cancel{ \dfrac{20}{2 } } }} \\ \\ \\ \colon\implies{\tt{AB = 10 \ m }}$

Hence,

• The height of the pole is 10 m.

More to Know:

• sin $\theta$ = 1/Cosec $\theta$
• cos$\theta$ = 1/sec $\theta$
• Cosec $\theta$ = 1/sin$\theta$
• tan $\theta$ = 1/cot $\theta$
• tan $\theta$ = sin $\theta$/cos $\theta$
• cot $\theta$ = cos $\theta$/sin $\theta$
• sec$\theta$ = 1/cos $\theta$
• tan $\theta$.cot $\theta$ = 1
• cos$\theta$.sec$\theta$ = 1
• cot²$\theta$ = Cosec²$\theta$ - 1