 In this video, part two of trigonometry, we are going to determine how to figure out the sizes of the sides, these guys here, using nothing but a side and an angle. So in this example, we're going to have 35 degrees for a designated angle, and we're going to have 250 whatever for our hypotenuse, and we're going to try to determine what this adjacent side is. So if we have adjacent, we have hypotenuse, and we have an angle, we should be able to remember from our last video that we're going to use cosine, because we have adjacent over hypotenuse, but we don't know what this is. So let's plug some numbers in, we'll work our way down the formula and see what happens. Let's remember that the cos of theta is equal to adjacent over hypotenuse. Let's start out with plugging the numbers that we know. So we know that the cos of theta is also the cos of 35 degrees is equal to the we don't know over 250. Let's transpose that now. However, before we transpose, let's just get rid of this cos 35. What we're going to do is just punch it in your calculator, and if you need to remember how to use the calculator, watch the last video. But instead of using our inverse cos, we're just going to go cos, hit the cos button, 35 degrees, and that gives us 0.819. 0.819 is equal to we don't know over 250. Now we can start at the transposition. We flip it around, so we're going to divide this guy out of here. We're going to move this guy over to here. So we end up with the unknown is equal to 0.819 times 250, because all we have to do is cross multiply. And we're going to get an answer of 205. So that's not that bad. Let's get that written in there. So basically it is just like using what we did in the last video, except now we just need to know what this side is. So we're using the same formula. We just have our unknown over here as opposed to our unknown being the angle. So that's using cos. So we're going to walk through all three as we did in the last one. So that's cos for our next one we're going to use. While looking at this here we have an opposite and we have adjacent and an angle. So to me it looks like we're going to use tangent. Tangent of theta is equal to opposite over adjacent. So let's plug the numbers in that we have. The tangent of 48 degrees is equal to 300 over what? We punch tan 48 in our calculator and we get 1.11 is equal to 300 over what? So we transpose that. Now we've got 1.11 times we don't know is equal to 300. So we have to make one more step in our transposition, which tells us that our unknown factor here or the what? Is equal to 300 divided by 1.11 and we get our value of 270. So let's get that plugged in there. So there you have it. Again just using tangent with what we know. Now it leaves us with one more. We've already done cosine and we've already done tangent. So let's mix it up a bit and we're going to finish strong with sine. Now you can tell we're going to use sine because we have an unknown here. We have our hypotenuse. So we have our opposite side, which is unknown. Our hypotenuse which is 750 and our angle which is 67 degrees. So our sine is equal to opposite over hypotenuse, which is shown right here. Sine of theta is equal to opposite over hypotenuse. Let's plug in the numbers so we can see what we're working with. The sine of 67 degrees, which is theta here, is equal to, we don't know what that is, but we do know that the hypotenuse is 750. So let's get rid of the sine of 67, punch sine 67 into your calculator and then you get 0.92 is equal to the unknown divided by 750. And we can just cross multiply. Let's take a look what's next. Using cross multiplication, we end up with our unknown is equal to 0.92 times 750, which gives us a numerical value of 690. So let's punch that into our side of triangle here. And there you have it, 690. So we've gone through them all. We've gone through tangent using a side and an angle. We've gone through cosine using a side and an angle. And now we've gone through sine using a side and an angle. It's not that hard once you have the concept of that sine is equal to opposite over hypotenuse. Cosine is adjacent over hypotenuse and tangent is opposite over adjacent. Once you've got that down, if you go through these couple videos a couple times and some worksheets, you should have no problem at all.