Question

The center of the circle below is at P. If the angle < APB measures 62 °, and the radius is 11 cm., find the length of the arc AB in cm.. (round to the nearest tenth)

Answer 1

We are given a circle, the radius, and the measure of the central angle that forms the arc we are interested in. Therefore, with that information, we can find the length of the arc as follows.

We know that the length of an arc is the total circumference of the circle multiplied by the fraction between the measure of the arc. In this case, the measure of the arc is the same as the central angle, 62, therefore we have as follows:

`\begin{gathered} Length\text{ }arAB=2\pi(11)\cdot(62)/(360) \\ Length\text{ }arAB=69.11\cdot(62)/(360) \\ Length\text{ }arAB=11.90 \end{gathered}`

Therefore, the correct answer is option d. = 11.9cm