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

Step-by-step explanation:

step 1

Find the circumference

The circumference of a circle is equal to

we have

assume

substitute

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 subtends a central angle of

so

using proportion

Let

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

The sum of all angles in a pentagon is 540 degrees. Now that we know that, we can begin our equation:

100+102+108+121+x=540

Now, let's combine like terms: 431+x=540

Now, let's subtract 431 on both sides to figure out what x equals: x=109

x=109

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