\( \def\dfrac#1#2{\displaystyle\frac{#1}{#2}} \def\solve#1{\begin{array}{rcl}#1\end{array} } \)

Home / 08 Trigonometric Functions / 40 Right Angle Trigonometry

In a right triangle, if we pick one of the two acute angles, the ratio of the various sides form the trigonometric functions we have come to know. The typical mnemonic is SOH-CAH-TOA:

\[\solve{ \sin\theta &=&\dfrac{\text{ Opposite }}{\text{ Hypotenuse }}\\ \cos\theta &=&\dfrac{\text{ Adjacent }}{\text{ Hypotenuse }}\\ \tan\theta &=&\dfrac{\text{ Opposite }}{\text{ Adjacent }} } \]
We can visualize this in a generic right triangle:

When working with right triangles, we can pretty much solve all missing information so long as we use a combination of the right triangle trigonometry and the Pythagorean Formula: \(a^2+b^2=c^2\).