Find the length of the radius if the arc length is 12 meters and the central angle is 85

Answer 1

I like to set these up as ratios. (Part of the circumference)/(total circumference) = (part of the degrees or radians)/(total degrees or radians).

Knowing that 2π⋅r, or π⋅d = circumference, and there are 360^o in a circle, our equation looks like this:

12/(2π⋅r) = 85/360. Since there's an equal sign in the middle, we can cross multiply to solve for r: 12⋅360 = 85⋅2π⋅r, and r = ∼79.833 m.

Hope that helps!