Unit 41: SohCahToa

Most high schools teach the mnemonic SohCahToa as a way of remembering basic trigonometry functions.  If you haven’t seen it, it simply lays out an easy way to remember sine, cosine, and tangent relationships of an angle.

So for angle x,

$$sine=;frac{opposite}{hypotenuse};;;;;;;;;cosine=;frac{adjacent}{hypotenuse};;;;;;;;;tangent=;frac{opposite}{adjacent}$$

You must have these memorized!

Here’s an example of how you might be asked to apply this.

In the figure above AC = 20, AD = 6 and DB = 10.  What is tan x equal to?

We would start by labeling our sides, and then calculating what BC is.  We could either recognize this as a 3-4-5 triangle (since we have sides of 20 and 16), or use the Pythagorean.  Either way, once we understand BC is 12, we can say (tan x=frac{opposite}{adjacent}=;frac{12}{16}=frac34) .  So our correct answer is (frac34) or .75.