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

Answer:

$0.46\pi\ radians$

Step-by-step 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

$\frac{2\pi}{31.4}=\frac{x}{7.2} \\ \\x=2\pi (7.2)/31.4\\ \\x=0.46\pi\ radians$