Question

on a circle of radius 2 feet, what angle would subtend an arc of length 9 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: Use the 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 \(s = 9\) feet and \(r=2\) feet. We can solve for \(\theta\) (in radians) by \(\theta=\frac{s}{r}\).

$$ \theta=\frac{9}{2} $$

Step2: Convert radians to degrees

The conversion formula from radians to degrees is \(\theta_{degrees}=\theta_{radians}\times\frac{180^{\circ}}{\pi}\). Substitute \(\theta = \frac{9}{2}\) into the formula.

$$ \theta_{degrees}=\frac{9}{2}\times\frac{180^{\circ}}{\pi}=\frac{810^{\circ}}{\pi}\approx257.83^{\circ} $$

Answer:

In radians: \(\frac{9}{2}\)
In degrees: \(257.83\)