Question

In the problem, $s$denotes the length of the arc of a circle of radius $r$subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=5$miles, $s=3$miles, $\theta =?$

Short answer

The required central angle$\theta =0.6radians$.

Step-by-step solution

Step 1. Given information

$r=5miles,s=3miles,\theta =?$

Step 2. Formula Used

For a circle of radius $r$, a central angle of $\theta$radians subtends an arc whose length $s$is

$s=r\theta$

Step 3. Calculation

We have,

$r=5milesands=3miles$

Now,

The length s of the arc is

$s=r\theta$

$\Rightarrow \theta =\frac{s}{r}$

localid="1646633319299" $$\begin{gathered} \Rightarrow \theta =\frac{3}{5} \\ \Rightarrow \theta =0.6radians \end{gathered}$$