Use the arc length formula and the given information to find r. s = 12 cm, θ = 36°; r = ?

Solution:

A central angle makes two intercepted arcs, a major and a minor arc. The measure of arc length ‘s’ is given by the formula s = r θ, where ‘r’ is the radius and θ is the central angle opposite the arc length and expressed in radians.

Given conditions are

s = 12 cm, θ = 36°

Convert θ from degrees to radians.

θ = 36°(π/180°)

θ = π/5

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

12 = r θ

12 = r × π/5

r = 60/ π = 19.1 cm

Use the arc length formula and the given information to find r. s = 12 cm, θ = 36°; r = ?

Summary:-

If s = 12 cm, θ = 36° then arc length r =19.1 cm