Question

A central angle θ in a circle of radius 4 m is subtended by an arc of length 5 m. find the measure of θ in degrees. (round your answer to one decimal place.)

Answer 1

`\theta=71.6\°`

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=2\pi r`

we have

`r=4\ m`

substitute the values

`C=2\pi (4)=8 \pi\ m`

step 2

Remember that

360 degrees subtends the arc of length
`8 \pi\ m` (circumference)

so

by proportion

Find the measure of θ by an arc of length 5 m

assume
`\pi=3.1416`

`(360)/(8\pi)=(\theta)/(5)\\ \\ \theta=360*5/8\pi \\ \\ \theta=71.6\°`