How to use trigonometry to find angles or lengths

Before starting any calculations it makes sense for the new practitioner to use the handy "soh-cah-toa" rule which means that you use:

- sine with the opposite and hypotenuse sides to the angle.

-cosine with the adjacent and hypotenuse sides to the angle.

-tangent with the opposite and adjacent sides to the angle.

The rules are all formulated such that sin(x) = (opposite side length)/(hypotenuse length) where I have used x to denote the angle. The cosine and tangent follow in the same pattern. To find one of the three bits in the equation, you simply rearrange to get the unknown on its own and then (hopefully) just plug this into your calculator. In the case where you search for the angle you must get your trigonometric function on its own and then use the inverse function to both sides of the equation so now you will have for example :

x = arcsin[(opposite side length)/(hypotenuse side length)] where x is the angle and arcsin[] denotes the inverse of sine.

Similarly you would use this method with tangent and cosine.