an arc has a central angle of 57.3 degrees. in a circle with a diameter of 24 cm. determine the length of the arc to the nearest whole centimetre.

Answer 1

The formula for arc length is

s= rθ

where θ is in radians

Instead of the radius, the problem gives us a diameter of 24 cm. That is easily converted by dividing by two to give us a 12cm radius.

The problem gives θ in degrees so we first need to convert from degrees to radians. We know from the unit circle that 2π = 360º and π = 180º. We can use unit conversion to find that we need to multiply 57.3º by π/180. In the equation that would look like:

s = rθ (π/180)

When we put in our numbers for the degree and radius we solve to find:

s = (12 cm) (57.3º) (π/180)

s = 3.82π cm

s = 12.0009 cm ≈ 12 cm