My younger son is working through Art of Problem Solving’s Precalculus book this year. Today we were working through some problems in chapter 4 on right triangle trig. He had been working through this section on his own while I was traveling last week.

One of the problems struck me as one that would make a nice project – the problem gives two lengths of a triangle plus an angle and asks you to calculate the area.

Since the angle is 30 degrees, his solution to the problem did not really use trig:

Now I changed the angle to 40 degrees. My expectation was that this change would not produce a solution that was all that different – wow was I wrong.