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# Pythagoras' Theorem and other Trigonometric Rules

### Pythagoras’ Theorem

Pythagoras' Theorem (for a right angled triangle) can be written as:  $\mbox{(perpendicular height)}^2 + \mbox{(base)}^2 = \mbox{(hypotenuse)}^2$

Consider now the right angle triangle with an angle of $$\theta$$:

Pythagoras' Theorem now can be written as:
\begin{eqnarray*}
a^{2} + b^{2} &=& c^{2}
\end{eqnarray*}

For example, find the missing side of a triangle with hypotenuse of $$10$$ and a base of $$6$$.

\begin{eqnarray*}
a^{2}+ b^{2} &=& c^{2} \\
a^{2}+6^{2}&=&10^{2} \\
a^{2}&=& 100 - 36 \\
a^{2}&=& 64 \\
a&=& \sqrt{64} \\
&=& 8
\end{eqnarray*}