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.

4. the radian measure of the angle
5. the area of a sector with that central angle

Answer 1

Part 1) The exact value of the arc length is

Part 2) The approximate value of the arc length is

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

`(10\pi )/(360)=(x)/(150)`

`x=10\pi *150/360`

`x=(25)/(6) \pi`
`in`

step 3

Find the approximate value of the arc length

To find the approximate value, assume

`\pi =3.14`

substitute

`(25)/(6)(3.14)=13.1`
`in`