SohCahToa

Tags

math

Is a relation between the lengths of a right angled triangle, its angle and the trigonometric functions.

\begin{figure}[ht]
  \centering
  \incfig{20210610022247}
  \caption{Annotated figure of a triangle with description of SOHCAHTOA}.
  \label{fig:sohcahtoa}
\end{figure}

In fig:sohcahtoa you can see where the fields used by SohCahToa come from. The hypotenuse is the longest side of the triangle and is opposite the right angle, the opposite side is opposite from the angle we know (or are using for sohcahtoa) and the final side is the adjacent.

SohCahToa is an anagram used to remember the form and order of the formulae shown below. It can be interpreted as 3 pyramids, the center character in each pyramid is built by multiplying the two supporting base characters. That is to say:

\begin{align*} l_{\text{O}} &= \sin \theta \times l_{\text{H}} \
l_{\text{A}} &= \cos \theta \times l_{\text{H}} \
l_{\text{O}} &= \tan \theta \times l_{\text{A}} \end{align*}