Question

A pendulum swinging through a central angle of 67 degrees completes an arc of length 7.2 cm. What is the length of the pendulum?

Answer 1

Answer:

6.2 cm

Step-by-step explanation:

We are given that

Central angle =67 degrees

Length of an arc=7.2 cm

We have to find the length of pendulum.

We know that

Radian measure=$\frac{\pi}{180}\times degree\;measure$

By using this formula

67 degrees =$\frac{\pi}{180}\times 67=\frac{67\pi}{180}$ rad

Arc length, s=$r\theta$

Where r=Radius of circle

$\theta$=Central angle (in rad)

s=Length of arc

Using this formula then we get

$7.2=\frac{67\pi}{180}r$

$r=\frac{7.2\times 180}{67\pi}=6.2 cm$

Hence, the length of pendulum=6.2 cm

Answer 2

Answer: length of pendulum is 6.16 cm

Step-by-step explanation:

The pendulum swings through a central angle of 67 degrees. The length of the arc formed by the movement of the pendulum is 7.2 cm. Therefore, the length of the pendulum will be the radius of the circle formed. The formula for determining the length of arc is expressed as

Length of arc = #/360 × 2 × π × r

Where

r = radius

π = constant whose value is 3.14

# = central angle

Therefore

7.2 = 67/360 × 2 × 3.14 × r

7.2 = 1.1688r

r = 7.2/1.1688 = 6.16 cm