Question

Circle O shown below has an arc of length 34 inches subtended by an angle of 2.1 radians. Find the length of the radius, x, to the nearest tenth of an inch.

Answer 1

16.2 inches

Explanation

the arc length is given by the formula:

$\begin{gathered} arclength=\theta r \\ where\text{ } \\ r\text{ is the radius } \\ \theta\text{ is the angle in radians} \end{gathered}$

so

Step 1

a)let

$\begin{gathered} r=x\text{ \lparen unknown\rparen} \\ angle=\theta=2.1\text{ rad} \\ arclength\text{ = 34 inches} \end{gathered}$

b) now, replace in the formula and solve for x

$\begin{gathered} arclength=\theta r \\ 34\text{ inches=2.1 rad*x} \\ divide\text{ both sides by 2.1 rad} \\ 16.19\text{ inches =x} \\ rounded \\ x=16.2\text{ inches} \end{gathered}$

therefore, the answer is

16.2 inches

I hope this helps you