Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
-A wheel with a 32-inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 14 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?
A) $25.1 ^ { \circ }$
B) $27.1 ^ { \circ }$
C) $23.1 ^ { \circ }$
D) $21.1 ^ { \circ }$

Question

Quizplus · Accepted Answer

The length of the arc is given by the formula $ s = r \theta $, where $ s $ is the arc length, $ r $ is the radius, and $ \theta $ is the angle in radians. Here, $ s = 14 $ inches and $ r = 32 $ inches. Solving for $ \theta $, we get $ \theta = \frac{14}{32} \approx 0.4375 $ radians. Converting radians to degrees, $ \theta \approx 0.4375 \times \frac{180}{\pi} \approx 25.1^\circ $.

Find the Length of the Arc on a Circle of Radius