Use the arc length formula and the given information to find r. s = 16cm, θ = 48°; r = ?

Solution:

The given conditions are ‘S’ = 16 cm, θ = 48°; r = ?

To express angle in terms of π radians, use the ratio of 180° to π radians

θ = 48 (π/180) 

θ = 4π/15

Using the above information in the formula to find the arc length, the radius r is

S = r.θ

s/θ = rθ/θ

r = s/θ

r = 16 / 4π/15 = 16 × 15/4π

r = 60/π

Take π = 3.14

⇒ r = 60/(3.14) = 19.11(approx)

Use the arc length formula and the given information to find r. s = 16cm, θ = 48°; r = ?

Summary:-

If s = 16 cm, θ = 48° then r = 60/(3.14) = 19.11(approx). To express angle in terms of π radians, use the ratio of 180° to π radians.