Question

On a circle of radius 8 feet, what angle would subtend an arc of length 7 feet?

Answer 1

≈ 50°

Explanation:

arc length is calculated as

arc = circumference × fraction of circle

let x be the angle subtending the arc, then

arc = 2πr ×
`(x)/(360)` , that is

7 = 2π × 8 ×
`(x)/(360)`

7 = 16π ×
`(x)/(360)` ( multiply both sides by 360 to clear the fraction )

2520 = 16π × x ( divide both sides by 16π )

`(2520)/(16\pi )` = x , then

x ≈ 50° ( to the nearest whole degree )