Question

A circles has radius 10 centimeters. Suppose an arc on the circle has length 8rmula1" title="\pi" alt="\pi" align="absmiddle" class="latex-formula"> centimeters. what is the measure of the central angle whose radii define the arc?

Answer 1

Answer:

The measure of the central angle whose radii define the arc is $\mathbf{\frac{4\pi }{5} }$

Step-by-step explanation:

Radius of circle = 10 cm

Length of arc = $8\pi$

We need to find Theta $\theta$

The formula used will be: $S=r \theta$

S= length of arc, r = radius and $\theta$ = angle

Putting values and finding \theta

$S=r \theta\\8\pi =10 \theta\\\theta=\frac{8\pi }{10} \\\theta=\frac{4\pi }{5}$

So, the measure of the central angle whose radii define the arc is $\mathbf{\frac{4\pi }{5} }$