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° (see Fig. 9.11).​

Answer 1

Height of pole is 10m

Answer 2

$\large \sf \pink{given}$

circus artist is climbing a 20 m long rope

$\color{orange}{find}$

it's height of the pole

$\color{aqua}{required \: answer}$

$\implies$ Let the height of pole is AB

That rope is tired at point C

$\implies$ Length of Rope = 20 m

$\implies$ Hence, AC = 20 m

and also we know that angle made by rope with the ground level = 30 °

Hence, $\angle$ACB = 30 °

$\implies$We know that to find Hight of pole that AB

Since the pole is vertical

$\angle$ACB = 90°

In right angle ABC

$\implies$$\sin$

C $= \frac{side \: opposite}{hypotenus}$

$\implies$$\sin30$

= \frac{AB}{AC}

$\implies$ \frac{1}{2} = \frac{AB}{20}

$\implies$ \frac{1}{2} × 20 + AB

$\implies$ 10 = AB

$\implies$AB = 10

$\huge \sf \pink{hence \: the \: hight \: of \: pole \: is10 \: m}$