Question

find the measure (in radians) of a central angle of a sector of area 16 square inches in a circle of a radius 3.0 inches

Answer 1

To find the measure of a central angle of a sector, use the formula for the area of a sector. theta = 32 / 9 = 3.56 radians.

Step-by-step explanation:

To find the measure of a central angle of a sector, you need to use the formula for the area of a sector:

Area = (theta/2) x r^2

In this case, the area is given as 16 square inches and the radius is 3.0 inches. Plugging these values into the formula, we get:

16 = (theta/2) x 3.0^2

Now, solve for theta:

theta = (16 x 2) / (3.0^2)

theta = 32 / 9 = 3.56 radians.