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The famous Pythagoren Theorm concerns right triangles.  If the legs of
the triangle have lengths x and y, and the length of the hypotenuse is z,
% the $ delimiter marks the start and end of a mathematical expression
then $z = \sqrt{x^2+y^2}$.

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There are many proofs of this result.

We can get the corresponding angles via inverse trig functions.  For
instance, the angle formed by the sides of length x and z above, which
we'll call $\theta$,   % here's a Greek letter
is

\begin{equation}
\theta = cos^{-1}(\frac{x}{z})  % note the need for braces around the -1
\end{equation}

% the parentheses in the above expression aren't quite big enough;
% instead, we could have the LaTeX code
% \begin{equation}
% \theta = cos^{-1} \left ( \frac{x}{z} \right)  
% \end{equation}
% try it yourself (don't forget to remove the % comment symbols first)

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