Question

find the length s and area a.
the length of the arc is 13.4 yards.
(round to three decimal places as needed.)

Explanation:

Step1: Convert angle to radians

First, convert $70^{\circ}$ to radians. We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. So, $\theta = 70\times\frac{\pi}{180}=\frac{7\pi}{18}$ radians.

Step2: Find the arc - length

The formula for the arc - length $s$ of a circle with radius $r$ and central angle $\theta$ (in radians) is $s = r\theta$. Here, $r = 11$ yd and $\theta=\frac{7\pi}{18}$ radians. So, $s=11\times\frac{7\pi}{18}=\frac{77\pi}{18}\approx13.402$ yd.

Step3: Find the area of the sector

The formula for the area $A$ of a sector of a circle with radius $r$ and central angle $\theta$ (in radians) is $A=\frac{1}{2}r^{2}\theta$. Substitute $r = 11$ yd and $\theta=\frac{7\pi}{18}$ radians. Then $A=\frac{1}{2}\times11^{2}\times\frac{7\pi}{18}=\frac{1}{2}\times121\times\frac{7\pi}{18}=\frac{847\pi}{36}\approx73.712$ square yards.

Answer:

The length of the arc $s\approx13.402$ yards.
The area of the sector $A\approx73.712$ square yards.