Now that we've learned how to find a missing angle, we're going to learn how to find a missing side using SOH, CAH, and TOA. So put on a happy face and read this tutorial!
Let's start with SOH
Get that goof ol' calculator and make sure its on degree! This method is pretty simple too, but pay attention so you don't get confused along the way. You're always going to have a right triangle with all these methods. When using SOH, CAH, or TOA to find a missing side length, you'll have one angle and one side length given to you. Here's how you'll work with SOH:
SOH broken down to its formula is Sin^1(Opposite/Hypotenuse). For this example, our given angle is labeled "angle" and our hypotenuse will be our given side length since to use SOH, you must have the length of your hypotenuse. Since Opposite is also included in SOH, the opposite side of the angle is the side length we are missing and need to find. Here's how to do that.
- Your formula is now Sin^1(Opposite/Hypotenuse) but to make it easier and faster to solve, you can set it up like this: HypotenuseSin(Angle)
- Put in your hypotenuses length in the calculator, then press Sin, enter the degree of your given angle after sin
- Press Enter
- The value shown will be the length of your missing side
Now let's go on to CAH
The broken down formula for CAH is Cos(Adjacent/Hypotenuse), but similar to SOH, to make the problem easier you can alter it to AdjacentCos(Angle). Here's how to get your answer from there:
- Type the length of your adjacent side, then press the Cos key, after that type the given angle
- Press enter
- The value shown should be your side length
Finally, let's work on TOA
Now your equation is technically Tan(Opposite/Adjacent) but in its simplest form it is OppositeTan(Angle). Now with that form, here's how to get your answer:
- Enter your opposite measurement, then press Tan, after typing that, key in your angle measurment
- Press Enter
- The value shown should be your missing side length