QuestionJuly 15, 2025

How long is an arc intercepted by the given central angle in a circle of radius 12.89 km? 150^circ The length of the intercepted arc is approximately square km (Round to the nearest hundredth.)

How long is an arc intercepted by the given central angle in a circle of radius 12.89 km? 150^circ The length of the intercepted arc is approximately square km (Round to the nearest hundredth.)
How long is an arc intercepted by the given central angle in a circle of radius 12.89 km? 150^circ The length of the intercepted arc is approximately square km (Round to the nearest hundredth.)

Solution
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Answer

33.65 km Explanation 1. Convert Angle to Radians Use the formula \theta_{radians} = \theta_{degrees} \times \frac{\pi}{180} to convert 150^\circ to radians. \theta_{radians} = 150 \times \frac{\pi}{180} = \frac{5\pi}{6} radians. 2. Calculate Arc Length Use the formula for arc length L = r \theta, where r is the radius and \theta is the angle in radians. L = 12.89 \times \frac{5\pi}{6}. 3. Compute the Value Calculate L = 12.89 \times \frac{5\pi}{6} \approx 33.65 km.

Explanation

1. Convert Angle to Radians<br /> Use the formula $\theta_{radians} = \theta_{degrees} \times \frac{\pi}{180}$ to convert $150^\circ$ to radians. <br /> $\theta_{radians} = 150 \times \frac{\pi}{180} = \frac{5\pi}{6}$ radians.<br /><br />2. Calculate Arc Length<br /> Use the formula for arc length $L = r \theta$, where $r$ is the radius and $\theta$ is the angle in radians.<br /> $L = 12.89 \times \frac{5\pi}{6}$.<br /><br />3. Compute the Value<br /> Calculate $L = 12.89 \times \frac{5\pi}{6} \approx 33.65$ km.
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