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?

a. 38.22

b. 40.25

c. 42.99

d. 46.37

Answer 1

Option a.

The approximate measure, in degrees, of the central angle is
`38.22\°`

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=2\pi r`

we have

`r=15\ m`

assume

`\pi =3.14`

substitute

`C=2(3.14)(15)`

`C=94.2\ m`

step 2

Using proportion

Find the central angle of the circle by and arc length of 10 m

Remember that the circumference of a circle subtends a central angle of 360 degrees

so

Let

x -----> the measure of the central angle in degrees

`(94.2)/(360)=(10)/(x)\\ \\x=360*10/94.2\\ \\x=38.22\°`