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Poor Calvin, but thanks for a mental distraction while the condo park replaced a slider in our unit in 14 degree weather. I put on my wooly thinking cap to stay warm, and proceeded to do some wooly thinking.
ReplyDeleteFor a little kid, this is one of those line segment problems that comes with a drawing. Without one it gets complicated.
For line segment ABC, x=5 so AC=10
For line segment ACB, x=5 so AC=10
For line segment BAC, 5=3x, so x=5/3 and AC is 10/3
If Calvin was taking some seriously advanced math, he'd know that this relation describes a triangle, and thus gives you a sinusoidal function as the angle of any one of the intersections goes from 0 to 180. Example: in triangle ABC, when angle B is 0 degrees and when angle B is 180 degrees, then side AC=10. When angle B is 90 then Pythagoras steps in and shows us that x=root(25/3) thus 2x (side AC) =2*root(25/3). I leave the determination of the function as an exercise for the reader (hint: consider using radians), which will be the same math whether it's angle A, B, or C that is increasing or decreasing.