You may know from a previous post that I'm teaching math, which has meant some serious brushing up for me. Much to my surprise, I've actually enjoyed reviewing geometry. This is probably due to the fact that I had a positive experience with it back in high school, so trying to dredge up those memories isn't as horrible as reliving various other high school moments. (Big shout out to Elaine Watson of Montpelier High for a fantastic sophomore geometry class!)
Today I am here to discuss my best friend, Mr. Right Triangle. Mr. Right Triangle comes in many forms - today he is appearing as a 45:45:90 triangle:
Triangle ABC is a right triangle with two 45 degree angles. You can also call it a right isosceles triangle. When we know the length of just one leg of this triangle, we can find the lengths of the other two legs.
For example, if:
AB = 3
then:
CB = 3
CA = 3√2
Got it? Now try using what we know about Mr. Right Triangle to solve the following classic problem. The lines that are exterior to the circle are tangent to the circle at points A and B. AB = 4. What is the area of the circle? (Formula for the area of a circle: A = ∏r2.) Hint: visualize Mr. Right Triangle. In fact, visualize him twice.
Stuck? Comment and I'll write back and help you out. Check back soon - Mr. Right Triangle will be appearing again on this blog in a different form.