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Solve Pythagorean Theorem for Unknown Leg Length

Use the Pythagorean Theorem to find the missing leg length of a triangle. Given two sides a = 7 and b = 6, find c. Is it a Pythagorean Triple? Practice with different side lengths. Remember to square, isolate, and undo to find the unknown.

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Solve Pythagorean Theorem for Unknown Leg Length

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  1. Use the Pythagorean Theorem to find a Leg a2 + b2 = c2

  2. a b c Find the Hypotenuse a = 7 b = 6 c = ? Is this a Pythagorean Triple? Nope! a2 + b2 = c2 72 + 62 = c2 49 + 36 = c2 85 = c2 9.21  c

  3. 17 a 15 Now find a leg a2 + 152 = 172 a2 + 225 = 289 square the known sides -225 = -225 isolate the variable a2 =64 subtract a = 64  “Undo” the square a = 8 Check!

  4. Check a2 + 152 = 172 82 + 152 = 172 substitute the variable you found 64 + 225 = 289 solve 289 = 289 It checks!

  5. 60 61 b Practice 602 + b2 = 612 602 + b2 = 612 3600 + b2 = 3721 -3600 = -3600 b2 = 121 b = 11 Is it a triple?

  6. 15 a 10 Practice a2 + b2 = c2 a2 + 102 = 152 a2 + 100 = 225 -100 =-100 a2 = 125 a = 125 a  11.18 Not a Triple!

  7. That’s all for today! Do your homework!

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