Arc Length in Degrees

Question

Alison is jogging on a circular track that has a radius of 140 feet. She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

Answer 1

Hey Brian,

Though they are two equations/formulas we can use to solve this problem, since the problem specifically asks for an answer in degrees, we will be using the following equation:

arc length = 2(pi)(r)(x/360) * where x would be the measure of minor arc RN in degrees as stated

Since we know that the radius = 140', and that the arc length from R to N is 230', we need only to solve for x. First, we can divide the arc length, 230', by 2(pi)(140') to isolate (x/360).

(230') / (2(pi)(140')) = (x/360)

Since we aren't working in radians, and the RHS of the equation is only a ratio between two values of degrees, we can then multiply both sides by 360 to isolate the desired value in degrees of the arc RN, x.

((230')(360)) / (2(pi)(140)) = x

Upon solving we get the value of:

x = 94.13 degrees

Which is exactly the value of the measure of minor arc RN. I hope this answers your question fully!!

Answer 2

measure of arc = circumference of circle

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degrees of arc 360 degrees

circumference of circle = 2 * PI * radius, where PI = 3.14

230 = 2* 3.14 * 140

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degrees of arc 360

degrees of arc = 230 * 360 / 879.2 = 94.17 degrees ~ 94 degrees