Question

A central angle of a circle with radius 150 cm cuts off an arc of 200 cm. Find each measure in Exercises 4 and 5.

Answer 1

Answer:

Part 1) The exact value of the arc length is

Part 2) The approximate value of the arc length is

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

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