Question

The arc length

shown below is 15 feet.
State the equation that relates arc length to central angle.
Find the angle
in radians.
Convert your answer from Part II to degrees and write it to the nearest hundredth of a degree.

Answer 1

• s = rθ
• 2.5 radians
• 143.24°

Explanation:

The applicable formula is ...

s = rθ

where s is the arc length, r is the circle's radius, and θ is the central angle in radians.

Filling in the given values, we find ...

15 = 6θ

θ = 15/6 = 2.5 . . . radians

Pi (π) radians is 180°, so the angle in degrees is ...

2.5(180°/π) ≈ 143.24°