We know that to find the length of an arc, we must multiply the radius of the circle times the interior angle of the circle (or central angle) so long as the central angle is in radians, not degrees. In circular trigonometry, we always measure in RADIANS. Make sure to convert first!
Today, we found the missing angle of a larger/smaller circle given the radius/central angle of another. To do this, we first found the missing arc length, then set it equal to the arc length of the other circle to solve for the missing central angle.
For a real-life application of this problem, we looked at gears on a clock and how they rotated together. Depending on the size of the gear, the gear rotated a different amount of total degrees (which we solved using the s = r times theta formula).
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