Simple trigonometry question (help)?

Question

Find the length of the arc on a circle of radius r intercepted by a central angle (theta).  Round answer to nearest 2 decimal places.

1. r = 3 meters, (theta) = 75deg

2. r = 55 inches, (theta) = 45deg

I know S=radius(theta), and the degrees *should* translate to 12pi/5  and pi/4 for each, however, when I plug them into the formula, both come out to an answer larger than the circumference.  2pi(3) for instance is 18.8, and 3 x 12pi/5 = 22.6

Where am I going wrong? And what are the correct answers?  Please show work.

Jakob · Accepted Answer

Your radian conversions are a little off, angle * pi/180, or (x)pi * 180/pi.

so its 5pi/12, and pi/4

So 3 * 5pi/12 = 5pi/4 = 1.25 * 3.14xxx = 3.9269908169872415480783042290994 Meters
    55in * pi/4 = 55pi/4 = 13.75 * 3.14xxx = 43.196898986859657028861346520093 inches

use this site to check against future errors
http://www.analyzemath.com/Geometry_calculators/arc_length_area_sector.html

PS
Debra D, 
Pi = 180 not 360

debra d · Answer

360 degrees divided by theta equals how many arcs of that length there would be in the entire circle,  therefore dividing the circumference by that number would be the length of one arc.
If theta is 75 degrees there would be 4.8 arcs in the entire circle (360 divided by 75 = 4.8)
If r = 3 meters  the circumference is 3.14 x 3 or 9.42 meters
9.42 divided by 4.8 =1.96 meters

If r =55 inches and theta equals 45
172.7 divided by 8 = 21.59 inches

Simple trigonometry question (help)?

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