The other day a friend called me up and asked me to help him figure out a "formula" to use to find the diameter of an attachment for a carbite tool he has. He's a machinist. If you can imagine this, he had an equilateral triangle and he only knew the height of the triangle. He needed to know the diameter of the circle that fit inside of the triangle so he could order the correct part to fit with the tool.
I didn't think that there was a pre-made formula to figure this out so I used knowledge of geometry and trigonometry to find the diameter. As a prospective math teacher I was so excited to see my mathematical knowledge put to the test. This was not a textbook problem, but one that was a real world application problem that could easily be used in a 3rd or 4th year algebra/trig class. The comment I made to my friend was that I could tell my students there are lots of applications of mathematics in the real world if we open our eyes to the possibilities.