SOLUTION: A 32-inch radius is marked as two points on the rim. The distance between the marks along the wheel is found to be 20 inches. What is the angle (to the nearest tenth of the degree)

Question 248960: A 32-inch radius is marked as two points on the rim. The distance between the marks along the wheel is found to be 20 inches. What is the angle (to the nearest tenth of the degree) between the radii to the two marks? The answer is 35.8 degrees but how do I solve this?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
A 32-inch radius is marked as two points on the rim. The distance between the marks along the wheel is found to be 20 inches. What is the angle (to the nearest tenth of the degree) between the radii to the two marks? The answer is 35.8 degrees but how do I solve this?
We have a theorem that says a central angle (one formed by two radii) subtends an arc of the same measure as the angle.
Since the circle has a radius of 32, the circumference C of the circle is given by:
C = pi times the diameter = pi*(2*radius)
In this case the radius is 32 so:
C = 64*pi
The arc represents 20/(64*pi) part of the circle.
Since there are 360 degrees in the whole circle, the arc, in degrees, must be:
(20/(64*pi)) * 360 =
7200/(64*3.1416) = 35.8 degrees

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