Question 10.

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Presentation transcript:

Question 10

Question 10 In right triangle ABC, side AC is longer than side BC. The boxed numbers represent the possible side lengths of triangle ABC. Identify three boxed numbers that could be the side lengths of triangle ABC. The students can use a calculator for this problem. Possible answers will be shown on the next slides. Students can receive up to 2 points for this problem: 2—Student correctly chooses a set of 3 side lengths 1—Student shows partial understanding by choosing 3 side lengths but putting them in the wrong order 0—Student does not get the right answer. To be able to answer this one, the students will need to know the Pythagorean Theorem. The Pythagorean theorem is a2 + b2 = c2. One of the things they need to remember is that the two sides (a and b) and smaller than the hypotenuse (side c). Without just knowing the answers, the students will need to guess in check in order to find the solution. There are three possible solutions: BC = 7; AC = 24; AB = 25 BC = 15; AC = 20; AB = 25 BC = 8; AC = 15; AB = 17

Question 10 Cont B 25 7 A C 24 72 + 242 = 252 49 + 576 = 625 625 = 625 72 + 242 = 252 Here is the first triangle where the sides are 7 and 24 and the longest side is 25. It also shows how to check to see that the answer is correct. To check to see if this one is correct, the two smaller sides are squared and then added together. If this equals the longest side squared, then it works out. 72 + 242 = 252. When you square everything, you get that 49 + 576 = 625. When you add together 49 and 576, you get that it is equal to each other so those numbers fit for a right triangle. 49 + 576 = 625 625 = 625

Question 10 Cont A B C 25 15 20 152 + 202 = 252 Here is the second triangle where the sides are 15 and 20 and the longest side is 25. It also shows how to check to see that the answer is correct. To check to see if this one is correct, the two smaller sides are squared and then added together. If this equals the longest side squared, then it works out. 152 + 202 = 252. When you square everything, you get that 225 + 400 = 625. When you add together 225 and 400, you get that it is equal to each other so those numbers fit for a right triangle. 225 + 400 = 625 625 = 625

Question 10 Cont B 17 8 A C 15 82 + 152 = 172 64 + 225 = 289 289 = 289 82 + 152 = 172 Here is the second triangle where the sides are 8 and 15 and the longest side is 17. It also shows how to check to see that the answer is correct. To check to see if this one is correct, the two smaller sides are squared and then added together. If this equals the longest side squared, then it works out. 82 + 152 = 172. When you square everything, you get that 64+ 225= 289. When you add together 64 and 225, you get that it is equal to each other so those numbers fit for a right triangle. 64 + 225 = 289 289 = 289