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Right Triangle Fun! 1. Get out a piece of paper. 2. Get out a pencil or pen. 3. Get out a calculator. Read each slide. Answer the questions The Pythagorean Theorem can be used to find the length of the missing side of a right triangle if you know the length of the other two sides. 5 12 X What kind of triangles does the Pythagorean Theorem work on? Acute Triangles Right Triangles Obtuse Triangles Any kind of triangle The formula for the Pythagorean Theorem is: leg2 + leg2 = hypotenuse2 5 12 X What in the world are Legs or Hypotenuse? Legs always make a right angle! They Hypotenuse must be the longest! L E G H Y P LEG O T E N U S E L E G H Y P LEG O T E N Which side must be the longest? U S E leg hypotenuse It doesn't matter which way the triangle is facing. The legs always make the right angle and the side opposite the right angle is always the hypotenuse. hypotenuse leg leg z Which side is the hypotenuse? (click on the correct answer) x x y y z z If you picked y, you were correct!!! x x y y z Which side is the hypotenuse? (click on the correct answer) x z y x z y Did you pick the right answer? x z x y None of these, it's not a right triangle! Which side is the hypotenuse? (click on the correct answer) x z y x z y Just because it looks like a right triangle, doesn't mean it is. It has to be marked or labeled or some way let you know there is a right angle! Did you catch my trickery? z x y So how do we use this Pythagorean Theorem to find the missing side of a right triangle? Well, we've covered the first step already. First we have to identify the legs and the hypotenuse. The legs have lengths 3 and 4 and we don't know how long the hypotenuse is. x 4 3 Once we've identified the legs and hypotenuse, we substitute these for the letters in the formula. leg2 + leg2 = hyp2 (3)2 + (4)2 = (x)2 x 4 3 So the hypotenuse is 5! Simplify and Solve First the exponents (3)2 + (4)2 = (x)2 9 + 16 = x2 25 = x2 √25 =√x2 5 = x Write this equation on your paper and solve. Make sure you show all your work! 52 + x2 = 132 Type your answer below! x = Did you get the right answer? Here's my work: 52 + x2 = 132 25 + x2 = 169 -25 -25 x2 = 144 √x2 =√144 x = 12 Which side is the hypotenuse? x 40 41 They're all hypotenuses! There isn't a hypotenuse! x 40 41 Formula: leg2 + leg2 = hyp2 41 was the correct answer! x x2 + 402 = 412 x2 + 1600 = 1681 - 1600 -1600 x2 = 81 √x2 = √81 x = 9 40 41 Now you try one: Which way should you set up the equation? (Pick one) (8)2 + (6)2 = (n)2 6 8 n (6)2 + (n)2 = (8)2 If you picked: (8)2 + (6)2 = (n)2 YOU'RE CORRECT!!! You could also write: (6)2 + (8)2 = (n)2 Write down the equation on your paper. (6)2 + (8)2 = (n)2 Which one of these show up in your work? Now solve your equation. 28 = n2 100 = n2 196 = n2 How long is the hypotenuse (c)? PICK ONE 100 50 10 100 = n2 is CORRECT!!! √10 = √n2 10 = n The hypontenuse is 10 units long. (15)2 + (17)2 = (x)2 Now you try one: Which equation is correct? (Pick one) 15 17 (15)2 + (x)2 = (17)2 x Which equation shows up in your work? If you picked: (15)2 + (x)2 = (17)2 YOU'RE CORRECT!!! You could also write: (x)2 + (15)2 = (17)2 x2 = 22 x2 = 352 x2 = 64 x = 8 which means the leg is 8 units long! x2 = 64 is CORRECT! So, which answer is correct? 15 17 x = 8 which means the hypotenuse is 8 units long! x √x2 = √64 x = 8 which means the leg is 8 units long is the correct answer! 15 17 x Let's try one more: Which way should you substitute the numbers? (Pick one) (13)2 + (5)2 = (m)2 13 5 m (m)2 + (5)2 = (13)2 Which is the correct simplification of the equation? (PICK ONE) If you picked: (m)2 + (5)2 = (13)2 YOU'RE CORRECT!!! You could also write: (5)2 + (m)2 = (13)2 m2 + 25 = 169 m2 + 10 = 26 What is the next step and the result? PICK ONE Subtract 25. m2 = 144 Take the square root of both sides. m + 5 = 13 m2 + 25 = 169 is CORRECT!!! 13 5 m You must subtract 25. √m2 = √144 m =72 units m =12 units m =144 units √m2 = √144 m = 12 The leg is 12 units long. The first equation should be x2 +252 =242 It's not a right triangle, so you can't use the Pythagorean Theorem The x2 =49 is wrong. I Have no idea x2 +242 =252 x2 +576=625 x2 =49 √x2 =√49 x = 7 Why is this problem WRONG? 24 25 x |