Question

The center of the circle below is at P. If the angle < APB measures 49 °, and the radius is 13 cm., find the length of the arc AB in cm.. (round to the nearest tenth)

Answer 1

Given:

• m∠APB = 49 degrees

,

• Radius = 13 cm

Let's find the length of arc AB.

To find the length of arc AB, apply the formula:

`L=2\pi r*(\theta)/(360)`

Where:

r is the radius = 13 cm

θ is the central angle = 49 degrees

Thus, we have:

`\begin{gathered} L=2\pi *13*(49)/(360) \\ \end{gathered}`

Solving further:

`\begin{gathered} L=(2\pi *13*49)/(360) \\ \\ L=(26\pi *49)/(360) \\ \\ L=(1274\pi)/(360) \\ \\ L=11.1\text{ cm} \end{gathered}`

Therefore, the length of arc AB is 11.1 cm.

• ANSWER:

d. 11.1 cm