Finding Angles with SOH
First off, you're going to need a graphing calculator. Go to mode and set your calculator from radian to degree. This is a crucial step! Now that we've set the calculator on radian, you want to locate your theta, or missing angle. This will often be represented as a 0 with a line through it. In the diagram above, theta is located in the top inner point of the triangle. Since SOH represents sine, opposite, and hypotnuse, you know you will be using the sine key on your calculator. Since you are finding an angle you will be using sine inverse.
- To switch to sine inverse, push the second key on your calculator, then press sine
The hypotenuse always stays the same, it is always the longest side length. The adjacent and opposite can change however depending on where theta is located. Opposite will always be the side length opposite theta, as seen in the diagram, and adjacent will always be a part of the angle.
That's enough background, lets see how to find this angle!
The breakdown or formula of SOH for angles is Sin^-1(Opposite/Hypotenuse). Lets say in this case the number for hypotenuse is represented by A and the number for Opposite is represented by C. You'll need your calculator for this part. Here's the steps to findind your missing angle:
- Click on 2nd, then Sin
- Enter the value of the opposite, then press the division sign and enter the value of the hypotenuse
- Press the equals key
- The value shown will be the value of your theta/missing angle
Now I'll Explain CAH
You're going to need your calculator still, and don't forget to make sure its in degree and not radian. The process of CAH is very much similar to that of SOH. Your theta is still located in the same place, only this time, imagine you only know the lengths of you adjacent and hypotenuse, not your opposite. Now instead of SOH, you'll be using CAH. The equation of CAH for an angle is Cos^-1(Adjacent/Hypotenuse). Here's the steps to finding your angle by using CAH:
- Press the 2nd key, then the Cos key
- Now enter the length of your adjacent side divided by the length of your hypotenuse
- Press Enter
- The answer that appears will be your missing angle
Now finally, TOA
Don't forget your calculator again, and remember DEGREE NOT RADIAN! Now this process is again very similar to SOH and CAH. The equation breakdown of TOA is Tan^-1(Opposite/Adjacent). Here's the steps to finding your angle through TOA:
- Press 2nd, then press Tan
- Enter your opposite length divided by your adjacent length
- Press enter
- The number shown is your missing angle