Question

What is the approximate measure, in degrees, of the central angle of the circle whose radius is 15 m and arc length is 10 m?

Answer 1

Answer:

$38.2\°$

Step-by-step explanation:

we know that

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=15\ m$

substitute

$C=2\pi (15)=30\pi\ m$

Remember that

$360$ degrees subtends the complete circle of length  $30\pi\ m$

so

by proportion

Find the approximate measure, in degrees, of the central angle of the circle whose radius is 15 m and arc length is 10 m

so

$\frac{360}{30\pi}=\frac{x}{10}\\ \\x=360*10/(30\pi)\\ \\x=38.2\°$