Solve the problem.
-Find the measure (in radians)of a central angle of a sector of area 55 square inches in a circle of radius 8 inches. Round to the nearest hundredth.
A)3.44 radians
B)2.58 radians
C)0.86 radians
D)1.72 radians

Question

Quizplus · Accepted Answer

The area of a sector is given by the formula $ A = \frac{1}{2} r^2 \theta $, where $ A $ is the area, $ r $ is the radius, and $ \theta $ is the central angle in radians. Plugging in the values, $ 55 = \frac{1}{2} \times 8^2 \times \theta $. Solving for $ \theta $, we get $ \theta = \frac{55}{32} \approx 1.72 $ radians.

Solve the Problem. -Find the Measure (In Radians)of a Central Angle of a Angle