Pythagorean Triple help! will medal

Question

jessicawade · Answer

Find the values of x and y that produce the following Pythagorean triples:
1.65,72,97
2.25,312,313
3.39,760,761

jessicawade · Answer

@StudyGurl14

studygurl14 · Answer

Is there a picture to go with this?

jessicawade · Answer

no im doing this for a project but i dont understand this question

anonymous · Answer

A Pythagorean triple is a set of three numbers $\{a,b,c\}$ that satisfies the Pythagorean relation:
$$a^2+b^2=c^2$$
By convention, the set is usually listed in such a way that $a\le b<c$.

anonymous · Answer

This means that in order to show that a given set is a Pyth triple, such as $\{3,4,5\}$, you would have to show that
$$3^2+4^2=5^2$$

jessicawade · Answer

ok

jessicawade · Answer

i just learned this so its kind of confusing hot to find the x and y lol

jessicawade · Answer

*how

anonymous · Answer

What are $x$ and $y$? Angles?

jessicawade · Answer

i think so

jessicawade · Answer

@SithsAndGiggles

jessicawade · Answer

the first one is x=13 and y=5

anonymous · Answer

|dw:1415640290200:dw|
You want to find the angles $x$ and $y$ that go with each triple $\{a,b,c\}$. It's a bit of trig.

anonymous · Answer

In this case,
$$\tan x=\frac{a}{b}\quad\text{and}\quad\tan y=\frac{b}{a}$$
For the first triple, you'd have $a=65$ and $b=72$.