NCERT Class X Chapter 9: Some Application Of Trigonometry Exercise 9.1 Question 1

NCERT Class X Chapter 9: Some Applications of Trigonometry

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°.

Given:

  • Length of the rope = 20 m
  • Angle made by the rope with the ground = \(30^\circ\)

To Find:

  • Height of the pole

Formula:

\[ \sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse}} \]

Solution:

Step 1: Let the height of the pole be \( h \) meters.

Step 2: In the right-angled triangle formed by the pole (vertical), rope (hypotenuse), and ground (base), apply the sine formula:

\[ \sin 30^\circ = \frac{h}{20} \]

Step 3: Substitute the value \(\sin 30^\circ = \frac{1}{2}\):

\[ \frac{1}{2} = \frac{h}{20} \]

Step 4: Solve for \( h \):

\[ h = 20 \times \frac{1}{2} = 10 \]

Result:

The height of the pole is \( 10 \) m.

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