Question
page 14 of 14 Radian Angle Measure Quick Check 2 of 52 of 5 Items Question If the arc of a circle is 15 meters long and the radius of the circle is 3 meters, then what is the measure of the central angle, to the nearest tenth of a degree, that intercepts that 15-meter arc?(1 point) Responses 353.4 degrees 353.4 degrees 7.9 degrees 7.9 degrees 286.5 degrees 286.5 degrees 282.7 degrees 282.7 degrees Skip to navigation
Answers
GPT-4o mini
To determine the measure of the central angle in degrees that intercepts an arc of a circle, we can use the formula:
\[
\theta = \frac{s}{r}
\]
where:
- \( s \) is the arc length (15 meters),
- \( r \) is the radius (3 meters), and
- \( \theta \) is in radians.
First, we can calculate the angle in radians:
\[
\theta = \frac{15 \text{ meters}}{3 \text{ meters}} = 5 \text{ radians}
\]
Next, to convert this angle from radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
\[
\theta_{\text{degrees}} = 5 \times \frac{180}{\pi} \approx 5 \times 57.2958 \approx 286.5 \text{ degrees}
\]
Therefore, the measure of the central angle that intercepts the 15-meter arc is approximately **286.5 degrees**.
So, the correct response is: **286.5 degrees**.
\[
\theta = \frac{s}{r}
\]
where:
- \( s \) is the arc length (15 meters),
- \( r \) is the radius (3 meters), and
- \( \theta \) is in radians.
First, we can calculate the angle in radians:
\[
\theta = \frac{15 \text{ meters}}{3 \text{ meters}} = 5 \text{ radians}
\]
Next, to convert this angle from radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
\[
\theta_{\text{degrees}} = 5 \times \frac{180}{\pi} \approx 5 \times 57.2958 \approx 286.5 \text{ degrees}
\]
Therefore, the measure of the central angle that intercepts the 15-meter arc is approximately **286.5 degrees**.
So, the correct response is: **286.5 degrees**.