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Math 10/11Triangles and TrigonometryTriangles are in some ways the simplest shape. (The math is the simplest)Pythagorean Theorem (We did this once before).-1390651168400Because a2+b2=c2You can always figure out a missing side. You square (multiply it by itself) the two sides you have. You add them an you have the missing side if it’s the long side. You square root the answer.405475120361400Square root is the opposite of a square: 52 is 25 Square root of 25 is 5. =5This isn’t quick to calculate by hand. Use the root button:30359355715Try to do this example on your calculator:If two sides are 3 and 4, the long side will be 5.BACKWARDS: If you know the long side and one other side you can do the same thing by Subtraction: c2-b2=a2 OR c2-a2=b2This is exactly the same thing.55549274872Tringles, Continued.Challenge Question: Explain how this diagram is a Mathematical Proof of the Pythagorean Theorem. Does it show that a2+b2=c2 is always true? This page has some striking GIFs about this: , we can easily find a missing side of a triangle.We can also find missing angles: All inside angles equal 180oIt is proved like this: B + C + A = a straight line. Imagine you know two of the angles, a and b, you can figure out c.180o – a – b = c. In this one you can rearrange the letters.180o – b – c = a.Here is a video: (These videos have almost every concept step by step for high school math). Trigonometry Reviewright4142Let’s start with Tan ratio.Here is a test problem. If one angle is 45o in a right triangle has to be 45o.This is just an example with easy numbers. Because two of the sides are the same and 1/1 is 1. Using the formula above you should be able to do 45o Tan or Tan 45o and the number 1. left508000Why learn Trigonometry?left42288200It is how we measured the earth, the orbits of the planets, the distance to the moon and the height of all the mountains. All of this made venturing to these places possible.Questions:Try online quiz on a2+b2=c2You should try at least 2 questions. More would be better. you already know trigonometry, do 1 to 5 of the advanced questions: of a TriangleFirst step is finding which side is which. This was like a2+b2=c2 because you need to know which is the long side:Here are your questions for this week:left857885 ................
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