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

Answer:

Option a.

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

Step-by-step 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

$\frac{94.2}{360}=\frac{10}{x}\\ \\x=360*10/94.2\\ \\x=38.22\°$