You can use the Pythagorean Theorem to find missing side lengths of right triangles and to solve interesting application problems. It is important to note that not all problems will have whole number answers. Round your answer to the nearest tenth unless you are told otherwise.

Example 1: The triangle below is a right triangle. Solve for x.

• The Pythagorean Theorem is ____?____
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  Check Your Answer

  a² + b² = c²
  
• Substitute the lengths of the legs values in for a and b: ____?_____
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  Check Your Answer

  8² + 12² = c²
  
• Square the numerical values:____?_____
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  64 + 144 = c²
  
• Add:____?____
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  208 = c²
  
• Take the square root of both sides: ____?_____
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  √208 = √c²
  
• Since 208 is not a perfect square, simplify to the product of the largest perfect square factor and the remaining factor: ____?_____
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  Check Your Answer

  √16 x 13 = √c² 
  
• Simplify both radicals: ____?_____ ***NOTE: Since the radicals represent lengths only the positive value is used.
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  4 √13 = c 
  
• Substitute x, the length of the hypotenuse, for c: ____?____
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  Check Your Answer

  x = 4 √13
  
• Use a calculator. Round to the nearest tenth: ___?____
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  Check Your Answer

  x = 14.4 

The length of the hypotenuse is 14.4.