# Week 7 – Calculating unknown angles (theta)

This week in math we learned how to calculate unknown angles of triangles given the sine, cosine and tangent ratios. The easiest way to remember these is the acronym SOH CAH TOA. The first letter stands for the ratio, and the second and third letters represents what lengths you put into the expression. When the expression is written, the second letter is in the numerator, and the third goes in the denominator.

To use the ratios you have to have your triangle labelled correctly. Then you can use the opposite, adjacent, and hypotenuse lengths to find your angle. These are the lengths represented by O, A, and H in SOH CAH TOA.

Example: In the triangle (see below) angle x is our unknown angle. Because we have at least 2 side lengths, we can find it. In this case the opposite and adjacent lengths will be used, so the tangent ratio will be the one we use. Then you simply set up the equation: $tan^-1$ (5/6), and plug it into your calculator. This gives us roughly 39.8° which will be rounded to 40°.