Consider circle Y with radius 3 m and central angle XYZ measuring 70°. What is the approximate length of minor arc XZ? Round to the nearest tenth of a meter.

Solution:

Presenting the problem statement in a diagram we have:

The ∠xyz =70˚

Converting 70˚ into radians we have

In radians 70˚ = π × (70/180) = (22/7) × (7/18) = 22/18 = 11/9 = 1.22 radians

We know that the angle θ is given as:

θ = s/r

where θ is in radians

s = arc xz

r = radius = 3m

1.22 = s / 3

Arc xz (s) = 3 × 1.22 = 3.66m

Summary:

Considering circle Y with radius 3 m and central angle XYZ measuring 70°. The approximate length of minor arc XZ is 3.66m