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.

$r=6$ meters, $s=8$meters, $\theta =?$

Short answer

The required central angle$\theta =1.33radians$

Step-by-step solution

Step 1. Given information

$r=6meters,s=8meters,\theta =?$

Step 2. Formula Used

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

$s=r\theta$

Step 3. Calculation

We have,

$r=6metersands=8meters$

Now,

The length s of the arc is

$$\begin{gathered} s=r\theta \\ \Rightarrow \theta =\frac{s}{r} \end{gathered}$$

$$\begin{gathered} \Rightarrow \theta =\frac{8}{6} \\ \Rightarrow \theta =1.33radians \end{gathered}$$