Question

1. -/1 points 0/2 submissions used find the degree measure of the angle with the given radian measure. (round your answer to one decimal place.) -6 ° 2. -/1 points 0/2 submissions used find the length s of the arc that subtends a central angle of measure 60° in a circle of radius 17 m. (round your answer to two decimal places.) s = m

Explanation:

Step1: Recall degree - radian conversion formula

The formula to convert radians to degrees is $\theta_{degrees}=\theta_{radians}\times\frac{180^{\circ}}{\pi}$. Given $\theta_{radians}=- 6$, then $\theta_{degrees}=-6\times\frac{180^{\circ}}{\pi}$.

Step2: Calculate the value

$\theta_{degrees}=-\frac{1080^{\circ}}{\pi}\approx - 343.8^{\circ}$ (rounded to one decimal place).

Step3: Recall arc - length formula

The arc - length formula is $s = r\theta$, where $r$ is the radius, $\theta$ is the central angle in radians. First, convert the angle from degrees to radians. Given $\theta = 60^{\circ}$, then $\theta_{radians}=60\times\frac{\pi}{180}=\frac{\pi}{3}$ radians, and $r = 17$ m.

Step4: Calculate the arc - length

Substitute $r = 17$ m and $\theta=\frac{\pi}{3}$ into the formula $s=r\theta$. So $s = 17\times\frac{\pi}{3}\approx17.80$ m (rounded to two decimal places).

Answer:

1. $-343.8$
2. $17.80$