Question

the arc length ($l_a$) of a sector of a circle with angle measure $x$ (in degrees) and radius $r$, is given by the equation $l_a=\frac{x}{360}cdot2pi r$. solve the equation for the radius of the sector, $r$.
$r = \frac{360cdot l_a}{2pi x}$
$r=\frac{2pi r}{360}cdot l_a$
$r=\frac{360cdot l_a}{2pi}$
$r=\frac{l_a}{2pi}-\frac{x}{360}$

Explanation:

Step1: Start with given formula

$L_a=\frac{x}{360}\cdot 2\pi r$

Step2: Isolate $r$

First, multiply both sides by $\frac{360}{2\pi x}$ to get $r=\frac{360\cdot L_a}{2\pi x}$

Answer:

$r = \frac{360\cdot L_a}{2\pi x}$