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g100num [7]
3 years ago
14

A circle has a radius of 5 in. A central angle that measures 150° cuts off an arc.

Mathematics
1 answer:
Slav-nsk [51]3 years ago
7 0

Answer:

Part 1) The exact value of the arc length is \frac{25}{6}\pi \ in

Part 2) The approximate value of the arc length is 13.1\ in

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

C=2\pi r

we have

r=5\ in

substitute

C=2\pi (5)

C=10\pi\ in

step 2

Find the exact value of the arc length by a central angle of 150 degrees

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

by proportion

\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in

step 3

Find the approximate value of the arc length

To find the approximate value, assume

\pi =3.14

substitute

\frac{25}{6}(3.14)=13.1\ in

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