 So now that you've learned what the inverse functions of sine, cosine, and tangent are, we are going to use those to set up trigonometric equations in order to solve for problems like 11 through 19. And the directions tell us that we're going to find the measure of angle A. So in every one of these problems we're going to find the measure of angle A. You're going to show the trig equation used to solve each problem. And there's a spot right here that says, oops sorry, that says what the steps would be. So the first thing that you want to do is write the trig ratio. So using Socatowa, write your trig ratio. And so if you look at number 11, we're trying to find angle A, which is this angle here. And you'll notice what you're given is the opposite side and the hypotenuse. We know 13 is the hypotenuse because it's across from the 90 degree angle. So if we are given the opposite leg and the hypotenuse, we know that that is sine. So what I'm going to do is I'm going to write sine of angle A equals opposite, which is 5 over hypotenuse, which is 13. So that's your first step is to write the trig ratio. Next what you want to do is use the inverse to find the angle. So that would be our second step. Use inverse to solve for A. Now of course if we're trying to find a different angle measure, it won't be solved for A. It would be solved for angle B or solve, and I'm going to actually put the angle measure right there. So use the inverse to solve for angle A in this problem. So what we're going to do is we are going to say that the inverse sine of 5 over 13 equals angle A. And then you just go right over to your calculator and find the answer to this inverse sine problem. And you should get angle A is equal to about 22.6 degrees. In number 12, again remember we are trying to solve for angle A, which is this angle. And so I'm going to set up my trig function or my trig ratio using the fact that I'm given the opposite and I'm given the adjacent. So that means I'm working with tan. So katoa tells me opposite over adjacent is tangent. So I'm going to write the tangent of A equals opposite, which is 6 over adjacent, which is 8. And then you just go to your calculator to plug that in. You do the inverse tan of 6 divided by 8. And you should get the angle A is about 36.9 degrees. By the way, remember that you can always check these when you're finished. And the way that you would check is just by plugging this answer back in for A. So on your calculator, if you type in tangent of 36.9, you should get, and it's going to be approximate. Remember we rounded 36.9. But you should get approximately 0.75 and 0.75 is equivalent to 6 over 8. So just keep that in mind when you take a quiz or a test. You can check to make sure that you got the correct angle measure. Okay, in this problem, again, we're still trying to find angle A, which is the top angle here. In this triangle, we are given the adjacent leg, which is 5 root 3. So we're given adjacent. And 10, since 10 is across from the 90 degree angle, that's the hypotenuse. So this time we are working with cosine. Cosine is equal to adjacent over hypotenuse. So I am going to go ahead and write my trig function, cosine of angle A equals 5 root 3 over 10. And you might want to simplify this just to make it easier when you plug it into your calculator, keeping in mind that if you have a ratio like this with 5 root 3 over 10, you can reduce that. And so we would have cosine of A equals root 3 over 2, because 5 goes into 5 once, 5 goes into 10 twice. So that might make it easier for you when you're punching it into your calculator. And we're going to just do inverse cosine of root 3 divided by 2. And you should get angle A is 30 degrees. Now what you might recognize, if you really think about this, what we talked about with our 30, 60, 90 triangles, remember in a 30, 60, 90 triangle if I say that this is my 60. Opposite the 30 degree is our shortest side x, and the hypotenuse is 2x, and opposite the 60 is x root 3. Well if you look at this ratio, root 3 over 2 would be root 3 over 2. And if we are paying attention to the fact that this has to be our 30 degree angle, if I can write on here, there we go, 30 degrees, we can see this is adjacent and hypotenuse. And so cosine of 30 degrees is root 3 over 2.