SOLUTION: The hypotenuse of a right triangle is sqrt 18 units. What are the lengths of the legs of the triangle? How many different answers can you find? Sketch a triangle for each answer. E

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Question 929582: The hypotenuse of a right triangle is sqrt 18 units. What are the lengths of the legs of the triangle? How many different answers can you find? Sketch a triangle for each answer. Explain your strategies.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If a & b are the two legs of the triangle, then a%5E2+%2B+b%5E2+=+%28sqrt%2818%29%29%5E2 which turns into a%5E2+%2B+b%5E2+=+18

Solve for b to get b+=+sqrt%2818+-+a%5E2%29

There are infinitely many ordered pairs (a,b) that make that equation true. If you sketch the graph of y+=+sqrt%2818+-+x%5E2%29 and make sure that 0%3Cx%3Csqrt%2818%29, then you'll see all of the possible combos of (a,b). Each combo is a point on the curve of the graph.