Math Class9 Newbook Ex6.2 q5

Math Class9 Newbook Ex6.2 q5 solution.

A 30 inch pendulum swings through an angle of 30 degree. Find the length of arc in inches through which the tip of the pendulum swings

To find the length of the arc through which the tip of the pendulum swings, we can use the formula for the length of an arc. $$\text{Arc length} = r \times \theta$$

$r$

r is the radius (length of the pendulum) in inches,

$\theta$

is the angle in radians.

First, we need to convert the angle from degrees to radians, because the formula uses radians.

$$\theta (\text{radians}) = \theta (\text{degrees}) \times \frac{\pi}{180}$$

• The length of the pendulum
  $r=\mathrm{30\; inches}$ 
• The angle
  $\theta = 30^\circ$ 

Step 1: Convert degrees to radians.

$$\theta (\text{radians}) = 30 \times \frac{\pi}{180} = \frac{\pi}{6} \, \text{radians}$$

Step 2: Calculate the arc length.

$$\text{Arc length} = 30 \times \frac{\pi}{6} = 5\pi \, \text{inches}$$

So, the length of the arc is:

$$\text{Arc length} \approx 5 \times 3.1416 = 15.71 \, \text{inches}$$

Thus, the length of the arc is approximately 15.71 inches.

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