In circle P diameter QS measures 30 cm. What is the approximate length of arc QR? Round to the nearest tenth of a centimeter a. 7.2 cm b. 25.8 cm c. 94.2 cm d. 14.4 cm PLEASE HU…

Question

asked Oct 25, 2021 225k views

1 Answer

Gabi Kliot · Answer 1 · 2021-10-29T21:54:41+0000

Given:

The diameter of the circle P is 30 cm.

The radius of the circle P is 15 cm.

The measure of ∠RPS is 125°

We need to determine the arc length of QR.

Measure of ∠QPR:

The angles QPR and RPS are linear pairs.

Thus, we have;

$\angle QPR + \angle RPS=180^(\circ)$

Substituting the values, we have;

$\angle QPR + 125^(\circ)=180^(\circ)$

$\angle QPR =55^(\circ)$

Thus, the measure of ∠QPR is 55°

Arc length of QR:

The arc length of QR can be determined using the formula,

$Arc \ length =((\theta)/(360))2 \pi r$

Substituting
$\theta=55$ and r =15, we get;

$Arc \ length =((55)/(360))2 (3.14)(15)$

$Arc\ length = (5181)/(360)$

$Arc \ length =14.4 \ cm$

Thus, the arc length of QR is 14.4 cm.

Hence, Option d is the correct answer.