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Related Rates Triangles 2

You might be struck by how similar this triangle looks to the one in "Related Rates Triangles 1". That's something that can cause students problems. A key thing to do is to tease apart what's different. Taking time to get your head wrapped around the situation is always a good thing to do! Be patient with yourself, it can take some head scratching.
1) Mess about with the sketch. How are the different parts of the triangle related to each other? How does moving things effect other things? (Your are just getting your head wrapped around what is happening. Very important!) 2) What's going on when you move point C? 3) Suppose that the length of AB=3 cm, AF =1.5 cm. If we know the length of FC, how could we predict the length of FG? 4) Again, suppose that the length of AB=3 cm, AF =1.5 cm, and that we know the length of FC. How would someone predict the lenth of GB? (You are writing a function here. Feel free to introduce a helpful variable.) 5) You may have noticed how angle CGF is also changing. Write a function for the measure of angle CGF in terms of the length of FC. Once again, suppose that the length of AB=3 cm, AF =1.5 cm. (Getting a bit more formal with the language here. We just want to be able to predict the the measure of the angle when we know the length of FC.)