One student wanted to average the two angles at 16 degrees each. Another said the observer could stand on a stool to be a little higher, so the angles would be 16 degrees each. Their answers were very close. There were other good (but wrong) methods that all came down to assuming this relationship was linear in a way that it’s not. Since their answers were very close, it was hard to help them see what was wrong with their reasoning.
She ends with “Can anyone help me here?” And she’s got some good comments. Here’s one from Kate Nowak:
This example you’ve picked is a toughie, for two reasons. As you point out, 18 and 14 degrees are both darn close to 16 degrees, so if you make that simplifying assumption 1) the problem is much easier and 2) the answer is pretty close to what it should be. But, you have to realize you are making a simplifying assumption that will throw your answer off a little bit, which I take it was not what your students were doing. They thought the result should lead to the exact, correct answer.
Anyone here have any ideas to send her way?