Ex. 9.1 Q1 Some Applications of Trigonometry Solution - NCERT Maths Class 10

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Question

A circus artist is climbing a \(20\,\rm{m}\) 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 \(30^\circ\) see Figure.

 

Text Solution

   

What is Known?

(i) Length of rope \(=\) \(20\,\rm{m}\) 

(ii) Angle of rope with ground \(=\) \(30^\circ\)\(=\) \(\angle ACB\)

What is Unknown?

Height of pole

Reasoning:

\(AB =\) Height of the Pole.

\(BC =\) Distance between the point on the ground and the pole.

\(AC =\) Length of the Rope (Hypotenuse).

We need to find the height of the pole \(AB,\) from the angle \(C\) and the length of the rope \(AC.\) Therefore, Trigonometric ratio involving all the three measures is \({\rm{sin}}\, C.\)

In \(\Delta ABC\),

\[\begin{align} {AB} &=\frac{\text { opposite }}{\text { hypotenuse }} \\ {\rm{sin}}\,C &=\frac{{AB}}{{AC}} \\ {\rm{sin}}\, {C} &=\frac{{AB}}{20} \\ \frac{1}{2} &=\frac{{AB}}{20} \\ {AB}&=\frac{1}{\not{2}} \times \not\!\!{20}^{10}\ \\ {AB} &=10 \rm {m} \end{align}\]

Height of pole \(AB = 10\rm\,m.\)