Please help me with this

Question

What is the length of an arc that is cut off by an angle of 210° in a circle of radius 5?

Answer 1

The trick for this question is to first convert degrees to radians. The conversion factor is π/180 radians/degrees. This is probably something that should be memorized when converting degrees to radians and the reciprocal when converting radians to degrees.

So 120 ° is 210π/180 = 7π/6 radians.

Another simple formula for arc length is S = rθ where θ must be in radians. For a radius of 5,

S= 5(7π/6) = (35/6)π.

When I taught math, I had my students leave the answer in terms of π, because it is exact or it will eventually cancel out if the answer was needed in further computations. However, this will depend on your instructor.

Answer 2

The formula for arc length is:

arc length = 2πr(θ/360) where

1. r = radius of the circle
2. θ = the angle rotated.

So, your arc length has a radius of 5 and an angle of 210 degrees.

The arc length can be found by substituting into the formula:

1. arc length = 2π(5)(210/360) = 35π/6 (exact answer)
2. or about 0.583π (decimal factor with π)
3. or approximately 1.833 (calculator answer)

Hope this was helpful,

Please leave a comment if helpful or not - especially if it wasn't helpful so that I can improve the answer.

David