This week in Math 10 we started our Trigonometry unit. In this blog post I will be showing how you find the angle of a triangle using trigonometry. To find the angle it only takes a few simple steps, but you need to be sure that you show your work and how you found your answer.
In my example I will be using this right triangle.
Step 1: First you need to label the sides of the triangle using the terms opposite, adjacent and hypotenuse. I recommend that you find the hypotenuse first by looking for the longest side of the triangle and note it is always across from the 90-degree angle. Next, I find the adjacent because I know it’s the side in between the angle you are looking for and the 90-degree angle. And finally, you have the opposite which is always across from the angle you are looking for.
Step 2: Next you need to identify if you are going to be using cosine, tangent, or sine. To easily find which one you are going to use the acronym “SOHCAHTOA”. In this case I can easily identify that I have to use my hypotenuse and my opposite side in this equation. So, I can go back and look at my acronym and see that “SOH” matches up with my sides because the “O” in it stands for “opposite” and the “H” stand for “hypotenuse.
Step 3: Now you are going to start your equation. You are going to start with “sin x” equals opposite divided by hypotenuse and how you know that is going back to “SOH” you can see “O” comes before “H” that is how you know which one is on top and what is on the bottom.
Step 4: Because you are finding the angle you are going to use inverse sine, which means when you write it out you put -1 above sin. In this step you are showing that inverse sin is being multiplies by 24/40.
Step 5: Now you are ready to put this equation in your calculator. You will put it in your calculator the same way it is on the paper. Because it is inverse sine you need to push shift and then put in your equation. (It is different on all calculators so identify what you need to do on yours)
Step 6: When you press equal on your calculator it is going to give you a number with a lot of decimals. Because you are finding an angle it is going to ask you to find the nearest degree. How you do that is look at the first number after the decimal, if it is 5 or bigger round up and if it is 4 or smaller round down.
(This photo wouldn’t go the right way but the decimal was 36.86989765)
Step 7: So because the decimal is 36.8 we are going to take that and round up to 37 degrees and that is your final answer.
Here is another example without breaking it down.
And just like that you can easily find the missing on every right triangle. Remember to write “SOHCAHTOA” on the top of your paper to help you out and remember to show your work!
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