Question

1. how long is the arc for an angle of 135° in a circle with a radius of 5 feet?

11.78 ft
23.24 ft
2.32 ft
84.94 ft

Explanation:

Step1: Convert angle to radians

The formula to convert degrees to radians is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 135^{\circ}$, then $\theta_{rad}=135\times\frac{\pi}{180}=\frac{3\pi}{4}$ radians.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $s$ is the arc length, $r$ is the radius, and $\theta$ is the angle in radians. Given $r = 5$ feet and $\theta=\frac{3\pi}{4}$ radians, then $s=5\times\frac{3\pi}{4}=\frac{15\pi}{4}\approx\frac{15\times 3.14}{4}=\frac{47.1}{4}=11.775\approx11.78$ feet.

Answer:

11.78 ft