SOLUTION: The hypotenuse of a certain right triangle has length 185 and one of its legs has a length of 57. Find the length of the other leg. Decide whether the answer is exact or just a

Algebra ->  Proofs -> SOLUTION: The hypotenuse of a certain right triangle has length 185 and one of its legs has a length of 57. Find the length of the other leg. Decide whether the answer is exact or just a       Log On


   

Question 12118: The hypotenuse of a certain right triangle has length 185 and one of its legs
has a length of 57. Find the length of the other leg. Decide whether the answer is exact or just a very good approximation.
To solve the first part of the problem, I used the pythagorean theorem, making the length of the other leg √30976= 176. How do I prove that this is exact or just an approximation?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
You did it right!

x%5E2+%2B+57%5E2+=+185%5E2
x%5E2+%2B+3249+=+34225
x%5E2+=+30976
x=+sqrt%2830976%29+=+176+

It is a special triangle in which all the sides come out to whole numbers. These numbers are called Pythagorean Triples, which can be derived with formulas from most any algebra book, even my own!!

The proof is that 176%5E2+%2B+57%5E2+=+185%5E2, and the equality is EXACT, not just approximate!!

R^2 at SCC