Question

standard 13 homework
score: 1/27 answered: 1/22
progress saved done
question 2
0/1 pt
on a circle of radius 8 feet, what angle would subtend an arc of length 4 feet? enter your first answer as an
integer or reduced fraction and round your second answer to 2 decimal places.
in radians:
in degrees:

Explanation:

Step1: Recall the arc - length formula

The formula for arc length \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius, and \(\theta\) is the central angle in radians. Given \(s = 4\) feet and \(r=8\) feet. We can solve for \(\theta\) (in radians) by rearranging the formula: \(\theta=\frac{s}{r}\).
Substitute \(s = 4\) and \(r = 8\) into the formula: \(\theta=\frac{4}{8}=\frac{1}{2}\) radians.

Step2: Convert radians to degrees

The conversion formula from radians to degrees is \(\theta_{degrees}=\theta_{radians}\times\frac{180^{\circ}}{\pi}\).
Since \(\theta_{radians}=\frac{1}{2}\), then \(\theta_{degrees}=\frac{1}{2}\times\frac{180^{\circ}}{\pi}=\frac{90^{\circ}}{\pi}\approx28.65^{\circ}\) (rounded to two decimal places).

Answer:

In radians: \(\frac{1}{2}\)
In degrees: \(28.65\)