Question

In the problem, $A$denotes the area of the sector of a circle of radius $r$formed by the central angle $\theta$.Find the missing quantity. Round answers to three decimal places.

Short answer

The required central angle$\theta$is localid="1647403790026" $0.24radian.$

Step-by-step solution

Step 1. Given information

$r=5miles,A=3squaremilesand\theta =?$

Step 2. Formula Used 

The Area $A$of the sector of a circle of radius $r$formed by the central angle of $\theta$radian is

$A=\frac{1}{2}{r}^2\theta$.

Step 3. Calculation

We have,

$r=5milesaandA=3squaremiles$

Now,

The area $A$of a sector is

$A=\frac{1}{2}{r}^2\theta$

$\Rightarrow 3=\frac{1}{2}\times 5^2\times \theta$

localid="1647403762702" $\Rightarrow 3=\frac{25}{2}\theta$

localid="1647403745535" $\Rightarrow \theta =0.24radian$