Question

Find arc length AB. Give your answer in terms of latex- and round to the nearest hundreth (2 decimal places).

Part a) State the general equation used to find arc length. (Do not include any measures given, just the general formula to find the any arc length)

Part b) Idenitfy the radius and the central angle of the circle below.

Part c) State the answer, arc length in terms of pi. And what does your answer represent (or in other words what does the arc length mean or represent) (2 points)

Answer 1

a) Arc length (s) is given in terms of radius (r) and central angle (θ) by
  s = r·θ . . . . . . . where θ is in radians

b) For the given circle and arc,
  r = 1.5 m
  θ = (160/180)π = 8π/9

c) s = (1.5 m)·(8π/9) = (4/3)π m
The arc length AB is the distance from A to B (or vice versa) along the circular path of radius 1.5 m centered on the red dot. (The arc length is the length of the arc!)