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jcherry99
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You can generate as many of these as you like by using this relationship
a = x^2 - y^2
b = 2xy
c = x^2 + y^2

Examples
x = 2 y = 1
a^2 + b^2 = c^2
a = 2^2 - 1^2
a = 4 - 1
a = 3

b = 2*2*1
b = 4

c = 2^2 + 1^2
c = 4 + 1
c = 5

So now you have a familiar example, the 3, 4, 5  triangle.
Check it
a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25

Another example (a little more complicated)
x = 7
y = 2
a = 7^2 - 2^2
a = 49 - 4
a = 45

b = 2xy
b = 2*7*2
b = 28

c = 7^2 + 2^2
c = 49 + 4
c = 53  This one is not well known.

a^2 + b^2 = c^2
45^2 + 28^2 = 53^2
2025 + 784 =? 2809
2809 = 2809

So this one is also a right angle triangle.
You cannot find a counterexample which will make this procedure untrue. Nice to have in your math kitbag. 
SpiderFoxImmortal

Answer:

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