Question

What is the measure in radians for the central angle of a circle whose radius is 5 and intercepted arc length is 7.2? Round your answer to the earnest hundredth. (THERE ARE NO ANSWER CHOICES. I HAVE TO TYPE THIS ANSWER OUT

Answer 1

`0.46\pi\ radians`

Explanation:

step 1

Find the circumference

The circumference of a circle is equal to

`C=2\pi r`

we have

`r=5\ units`

assume

`\pi=3.14`

substitute

`C=2(3.14)(5)=31.4\ units`

step 2

Find the measure in radians for the central angle of a circle whose radius is 5 and intercepted arc length is 7.2 units

Remember that

The circumference of
`31.4\ units` subtends a central angle of
`2\pi \ radians`

so

using proportion

Let

x-----> the central angle in radians

`(2\pi)/(31.4)=(x)/(7.2) \\ \\x=2\pi (7.2)/31.4\\ \\x=0.46\pi\ radians`