Solve the problem.
-A circular sector has an area of 17 in $^ { 2 }$ and an arc length of 3 inches. What is the measure of the central angle in degrees? Round to the nearest degree.
A) $30 ^ { \circ }$
B) $8 ^ { \circ }$
C) $15 ^ { \circ }$
D) $5 ^ { \circ }$

Question

Quizplus · Accepted Answer

The area of a circular sector is given by $ \frac{1}{2} r^2 \theta $ (where $ \theta $ is in radians) and the arc length is given by $ r\theta $. Given the area $ A = 17 $ in$^2$ and arc length $ L = 3 $ in, we can set up the equations $ \frac{1}{2} r^2 \theta = 17 $ and $ r\theta = 3 $. Dividing the area equation by the arc length equation gives $ \frac{1}{2} r = \frac{17}{3} $, solving for $ r $ gives $ r = \frac{34}{3} $. Substituting $ r $ back into $ r\theta = 3 $ gives $ \theta = \frac{3}{r} = \frac{3}{\frac{34}{3}} = \frac{9}{34} $ radians. Converting $ \theta $ to degrees: $ \theta_{degrees} = \frac{9}{34} \times \frac{180}{\pi} \approx 15^\circ $.

Solve the Problem 2^ { 2 }2 And an Arc Length of 3 Inches

Solve the Problem $^ { 2 }$ And an Arc Length of 3 Inches