Question

A central angle θ in a circle of radius 7 m is subtended by an arc of length 8 m. Find the measure of θ in degrees. (Round your answer to one decimal place.) θ=

Answer 1

θ ≈ 65.5°

Explanation:

the arc length (l) is calculated as

l = circumference of circle × fraction of circle

= 2πr ×
`(0)/(360)` ( r is the radius )

given r = 7 and l = 8 , then

8 = 2π × 7 ×
`(0)/(360)` ( multiply both sides by 360 to clear the fraction )

2880 = 14π × θ ( divide both sides by 14π )

`(2880)/(14\pi )` = θ , then

θ ≈ 65.5° ( to 1 decimal place )