Step by step directions for finding the angle measure using trig functions.

How to use your trig functions to find the angle?
Hope by now you have sine,cosine and tangent. These are your trig ratios. Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, Tangent is opposite over adjacent.
You can remember these using SOH CAH TOA
How do you find the angle measure? Follow these steps.
From the unknown angle, decide which two sides you have. That will help you decide which trig function to use.( Sin,Cosine,Tangent)
For example if I have opposite and hypotenuse I'm going to use the sin function. You look at the two you are given or if you have adjacent and hypotenuse you would use cosine. Then you set up the problem, and instead of the variable being x in the proportion the variable will be at the angle. Then solve using the 2nd function key to solve.
Lets go through some practice problems.
Practice 1. Find angle measure of D Let's look at our triangle. We have a D up here, a 28 here, and a 45 here. I will label E and F What we need to do first is decide which is our unknown angle. It will be D and from this angle which two sides do we have? Well this side is opposite and we are not using it. We have adjacent and the hypotenuse. So which trig function should we use? Adjacent and hypotenuse, so you would use Cosine. The cosine of which angle? We don't know which angle so the cosine of D = adjacent over hypotenuse so 28 over 45 So that is my first two steps. Let's go back and reference. From the unknown angle which was D we need to decide which two sides we had and we had adjacent and hypotenuse and we decided we are using the Cosine function. Then we set it up. Now we will solve it. We will set it up different. When looking for an we will work backwards, so we will use our inverse button. You can convert the fraction to a decimal or we can just put the inverse of the fraction also. I will show you both methods. Take cosine to -1 of 28/45) that is the fractional way If yo like the decimal way you can convert the fraction to a decimal. 28/45 = .62. You can also take the cosine of .622 repeating. I will go ahead run through that 2nd function,of cosine, and put in my fraction,28/45 and the angle measure is 51.52 or round this up to 52 degrees. So D = 52 degrees and I have my angle.

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