Question

standard 13 homework
score: 0/27 answered: 0/22
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question 1
on a circle of radius 8 feet, what angle would subtend an arc of length 12 feet? enter your first answer as
an integer or reduced fraction and round your second answer to 2 decimal places.
in radians:
in degrees:
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Explanation:

Step1: Use the arc - length formula

The arc - length formula is \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius of the circle, and \(\theta\) is the central angle in radians.
Given \(s = 12\) feet and \(r=8\) feet. We can solve for \(\theta\) (in radians) by \(\theta=\frac{s}{r}\).
Substitute \(s = 12\) and \(r = 8\) into the formula: \(\theta=\frac{12}{8}=\frac{3}{2}\) radians.

Step2: Convert radians to degrees

The conversion formula from radians to degrees is \(\theta_{degrees}=\theta_{radians}\times\frac{180^{\circ}}{\pi}\).
Since \(\theta=\frac{3}{2}\) radians, then \(\theta_{degrees}=\frac{3}{2}\times\frac{180^{\circ}}{\pi}\).
\(\theta_{degrees}=\frac{270^{\circ}}{\pi}\approx\frac{270}{3.14159}\approx 85.94^{\circ}\)

Answer:

In radians: \(\frac{3}{2}\)
In degrees: \(85.94\)