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Expert-verified Found in: Page 479 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # A sector of a circle of radius 80 miles has an area of $\mathbf{1600}{\mathbf{\text{\hspace{0.17em}miles}}}^{\mathbf{2}}$. Find the central angle (in radians) of the sector.

The central angle for the given radius and the circular area is $\frac{\mathbf{1}}{\mathbf{2}}$ radian.

See the step by step solution

## Step 1. Given information.

Area $\text{A}=1600{\text{\hspace{0.17em}miles}}^{2}$ and the radius $r=80$ miles.

## Step 2. Write down the concept.

Use the formula of the circular area $\text{A}=\frac{1}{2}{r}^{2}\theta$.

## Step 3. Determining the angle

Central angle $\theta =\frac{2A}{{r}^{2}}$

$\theta =2×\frac{1600}{{80}^{2}}$

$\theta =\frac{1}{2}$ radian. ### Want to see more solutions like these? 