Question

find the measure (in radians) of the central angle. the area of a sector is 12 sq units. picture is not drawn to scale. the measure is radian(s) (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{1}{2}r^{2}\theta$, where $A$ is the area of the sector, $r$ is the radius of the circle, and $\theta$ is the central - angle in radians.

Step2: Identify given values

We are given that $A = 12$ square units and $r = 4$ units.

Step3: Substitute values into formula

Substitute $A = 12$ and $r = 4$ into the formula $A=\frac{1}{2}r^{2}\theta$. We get $12=\frac{1}{2}(4)^{2}\theta$.

Step4: Simplify the equation

First, calculate $(4)^{2}=16$. Then the equation becomes $12=\frac{1}{2}\times16\theta$. Since $\frac{1}{2}\times16 = 8$, the equation is $12 = 8\theta$.

Step5: Solve for $\theta$

Divide both sides of the equation $12 = 8\theta$ by 8. So, $\theta=\frac{12}{8}=\frac{3}{2}=1.5$ radians.

Answer:

$1.5$