 Hi, I'm Brad Langdell and in this video I'm going to talk to you about the three trig ratios you should know for physics 20. Here's an example. We've got a triangle and we're going to solve for the side x. We know one side of the triangle is 4.0 units long and we know the angle down there is 56 degrees. Here's the two steps you're going to need to solve this problem. Number one, you want to name the sides of the triangle. This is often the part where students run into trouble. It's tricky because the opposite and adjacent sides of the triangle flip depending on which angle you're looking at. So start off by identifying an angle you want to use in your calculation. Here I'm going to use 56 degrees because that's the angle that's given and look at the side that's across from that angle. That will be the opposite side of the triangle. So in this example the opposite side will be what we're solving for. It'll be x. Now starting from your angle again look at the side of the triangle that is right next to the angle. That's going to be your adjacent side. So in our example the adjacent side is 4.0. Once you've named the sides step two is to match those sides to a trig equation and to go through and solve it. So in this case because I have opposite and adjacent I'm going to use the tan ratio. Tan of the angle theta equals opposite over adjacent. I can put in 56 degrees for the angle theta. The opposite side is x and the adjacent side is 4.0. To solve that equation I multiply both sides by 4 and I get that x will be whatever 4 multiplied by the tan of 56 degrees is which will work out to 5.9. Let's look at another triangle. Again we're going to solve for the side x but in this case when we name our sides we see that the x is the hypotenuse. I know this because it's the longest side and it's across from the right angle in the triangle. The side that I have given for me is the opposite side. It's across from the 59 degree angle that I'm going to use my calculation. So in step two I need to find a trig equation that has both opposite and hypotenuse in it which is the sine equation. I'm going to substitute in for the angle 59 degrees and make the opposite side 3.0. Then I can substitute in x for the hypotenuse. To rearrange this I get that x is equal to 3 divided by sine of the angle so that means the unknown side is 3.5 units long. In our last example we've got a triangle where we don't know the angle but we do note who the sides. So what we need to do in this case is again start by naming the sides. I have 8 being the side that is next to the angle so that's the adjacent side and I have 12 being the side that is across from the angle so that makes it the opposite side. Just like before I'm going to find a trig ratio with opposite and adjacent which is the tan ratio and just like before I'm going to substitute in opposite and adjacent sides but the difference here is I've got to find the angle. So the way I write this is by saying the angle is equal to the inverse tan or the tan to the negative one of 12 over 8 and we're going to type that into our calculator by pressing second and then the tan button then 12 over 8. This will give you 56 degrees.