Warmup 2/(The length of the third side of this triangle, rounded to the nearest whole number)
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1 Created by Max Robinson Warmup 2/(The length of the third side of this triangle, rounded to the nearest whole number) x 5 28 ***Get a calculator. Yellow or blue doesn t matter*** 1) Estimate how many feet are between home plate and second base on a baseball field. The bases are 90 feet apart. 2) Why is something to the second power called squared? (There is an actual reason, besides They just randomly decided to use that word. )
2 Go over homework 1) ABCDEFGHIJKLMNOPQRSTUVWXYZ 2) H, I, N, O, S, X, Z 3) O, X 4) A, H, I, M, O, T, U, V, W, X, Y 5) B, C, D, E, H, I, K, O, X 6) M W, b q, d p, u n
3 Go over homework 7) Some examples: TOT, WOW, MOM, YAY 8) Some examples: BED HIKE CHECKBOOK EXCEEDED KICKBOXED 9) Some examples: NOON SIS MOW pod suns swims ipod!
4 Angles Quiz Retake deadline Is tomorrow!!! You should turn corrections in by today.
5 Table of Contents (2 nd Semester) p. 1 Exponent Basics (1.2) p. 2 Multiplying and Dividing Powers (1.3) p. 3 Power to a Power (1.4) p. 4 Zero & Negative Exponents (1.5) p. 5 Scientific Notation (1.6) p. 6 Calcluating with Scientific Notation (1.7) p. 7 Angle Basics p. 8 Angles formed by Parallel Lines (5.1) p. 9 Transformations ( ) p. 10 Rotations (Handout) p. 11 Reverse Transformations p. 12 Pythagorean Theorem
6 Objective: Pythagorean Theorem Use the Pythagorean Theorem to find sides of a right triangle 12
7 Question: If you walk from corner to corner of a field that is exactly 1 mile by 1 mile, how many miles did you walk? 1 mile? 1 mile
8 PYTHAGOREAN THEOREM In a right triangle, a 2 + b 2 = c 2 a c a and b are the legs (the two sides connected to the right angle) c is the hypotenuse (the longest side, always across from the right angle) NOTE: It doesn t matter which leg is a and which is b; you will get the same answer either way) b
9 Example 1: Finding the Hypotenuse x 6 8 a 2 + b 2 = c 2 Write the equation = x 2 Substitute in the side lengths = x 2 Square the numbers. 100 = x 2 Add. 100 = x 2 Square root both sides. (Think: what times itself equals 100?) 10 = x The missing side length is 10. Now LOOK BACK at your triangle to make sure your answer is reasonable!
10 IMPORTANT NOTE It is very easy to remember a 2 + b 2 = c 2. But remembering this is meaningless unless you remember what a, b, and c are and when this equation is used. This equation is ONLY USED IN RIGHT TRIANGLES. a and b are the lengths of the two legs. c is the length of the hypotenuse.
11 Example 2: Finding a Leg x 7 12 a 2 + b 2 = c 2 Write the equation x 2 = 12 2 Substitute in the side lengths x 2 = 144 Square the numbers. x 2 = 95 Subtract 49 from both sides. x 2 = 95 Square root both sides. (Think: what times itself equals 95? This one will be a decimal, so use a calculator) x 9. 7 You can round your answer to the nearest tenth. Now LOOK BACK at your triangle to make sure your answer is reasonable! EXACT ANSWER: x = 95 ROUNDED ANSWER: x 9. 7
12 Three strategies to catch mistakes: 1. MAKE SURE YOUR ANSWER IS REASONABLE. 2. MAKE SURE YOUR ANSWER IS REASONABLE. 3. MAKE SURE YOUR ANSWER IS REASONABLE.
13 For this section We WILL be using calculators. Calculator Expectations: If you have your own, you should bring it. You may not use the calculator on your phone. (During class) ALWAYS PUT THE CALCULATOR BACK!!!
14 Unless I tell you otherwise I would like you to round to the nearest tenth. This is to help you see if your answer is reasonable. However, if I ask for an exact answer, this means you should leave it as a square root.
15 Example 3 Discuss with your group how to solve this problem. Estimate what you think the length of the third side would be. x 11 8 Trick question you don t know it s a right triangle!!!
16 Question: Would this be a right triangle? Nope:
17 QUESTION: HOW FAR does the catcher throw the ball when trying to catch a runner stealing 2 nd?
18 Back to this If you walk from corner to corner of a field that is exactly 1 mile by 1 mile, how many miles did you walk? 1 mile? 1 mile
19 HOMEWORK Pythagorean Theorem Worksheet Use the back or attach a separate sheet if you need more room
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