Pythagorean Theorem

Missing Side of Triangles

precalc 7


Here’s a mistake from a trig class. Would the question be easier in a Geometry class?

Here’s my theory: teachers underestimate how weak most of our students’ knowledge is, and how weakly in transfers. In particular, this problem became twice as difficult as soon as it was offered in the context of a trig class, without carefully writing the right angle in there with the lil’ square.

Am I right? Wrong?

Thanks to the Uncanny Tina Cardone for the submission.

One reply on “Missing Side of Triangles”

This problem is easily solved using law of sines, and simplifies beautifully because sin(90)=1. Many students took this approach, which is an extra step over using right triangle trig, but I was happy to see it. This student didn’t take the traditional trig approach and really over-thought the problem. The CAH shows they thought about triangle trig, which should have worked. They mis-applied the pythagorean theorem (perplexing because the diagram isn’t misleading, and they drew their own picture which shows the right angle even more clearly). Plus they mixed up a and A? So many questions…

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