An AMC 10 problem with some neat lessons about a 15-75-90 right triangle

This problem (#22 from the 2014 AMC 10a) gave my son some trouble this morning:

Screen Shot 2018-01-15 at 8.05.30 PM

We ended up having a nice talk about the problem this morning. To see if the ideas really sunk in, I asked him to talk through the solution tonight, and he did a nice job:

After we finished, I wanted to go back to the 2014 AMC 10 and just happened to notice that google was also showing that Art of Problem Solving had a video about the problem. So, I thought it would be fun to watch Richard Rusczyk’s solution. Turned out to be a lucky decision since his solution was totally different than the one we found:

It was neat to see this second solution – I learned a lot about 15-75-90 triangles today!

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