 Going back to the trig functions, when they say sine theta is opposite of our hypotenuse, what you've got to understand is theta is a neutral angle. So what you have to do is look at your drawing that you have and think about which angle you want to find out. Now with triangles, the things to keep in mind is the sum of the angles is equal to 180. So if this one's 30 degrees and this one's 90 degrees, 30 plus 90 is 120. You subtract that from 180, 120 minus 180 is 60. So automatically, you know what this angle is. So for any triangle, if they give you two angles, you know what the third angle is because all you got to do is take 180 and subtract the other two angles. The other thing is there's six pieces of info in a triangle. You've got three angles and three sides. If you know any three of these, one of them has to include a side. You can solve the triangle, which means find out what all the other angles are or how the other sides are. So if they give you one side and two angles, you can find out the other two sides and the other angle. If they give you one angle and two sides, you can again find out the other two angles and the other side. All you need is three pieces of info and one of them has to be a side. So for example, let's say they give you some piece of info where they say, let's change these to actual numbers and see how we're going to solve the triangle. One of the first things they do in math is they give you a question and say, solve the triangle. When they say solve the triangle, they want you to find all the other sides and all the other angles. So for them to tell you to solve the triangle, they have to give you at least three pieces of info, one of them being a side. So for example, let's deal with 30 degrees and let's say this is 7. Now 30 degrees and 7, where is our third piece of info? Our third piece of info is the right angle. This is 90 degrees. So whenever they tell you that you have a right triangle, they're already giving you one piece of info, which is 90 degrees. Now if you know this is 30, we know that the sum of the angles in a triangle is 180, then all you do is go 90 plus 30 is 120. 120 minus 180 is 60, okay? So if you know two pieces of information, you can get the third one. What I'm going to do is I'm going to change up the colors here so you know which pieces of info we have and which ones we're solving for. So this was 30 that was given. This is 7 that was given. And this is right angle, which is 90. So we just solved for one of the angles. Now what we want to do is solve for these two sides. Let's call these x and y, okay? The way we're going to do this is we're going to have to decide which side we want to solve. So this is mentally you're going to have to make a choice. Do you want to solve for x or y? Well, let's decide that we're going to solve for y, okay? So we want to solve for y, then you got to decide which angle you're going to use. Are you going to use the 60 degree angle or are you going to use a 30 degree angle? It's up to you. Now you stay away from the 90 degrees. The 90 degrees you're using as a reference to, for you to understand that this is a right triangle, okay? You never deal with the 90 degree angle in these functions, okay? Or in these operations, okay? So let's say we want to solve y and we're going to use angle 60. So what you do is mentally you put yourself at angle 60. So if you're sitting here, which one of these are you going to be able to use? Now, 60 degree is going to be your theta. That's your general angle. You have the hypotenuse. So you take a look at these functions. And the only two that have the hypotenuse are sine and cosine. You can't use tangent because it's got opposite over adjacent. So you're going to use 60 degrees and the only side that they're giving you, which is the hypotenuse. So we're either going to use this or this. Now since we chose to use sine, since we chose to use 60 degrees, that means y is adjacent to the 60 degree angle. Now some people confuse themselves and say, oh, this is also adjacent to 60 degrees as well. But this is the hypotenuse. So this doesn't count as being adjacent. This is always the hypotenuse. So the y becomes the adjacent. The x is opposite from 60. So if we're going to use 60 degrees, we're going to use the adjacent one. So we're going to use cos. So what we're going to do is say, okay, we're going to use this function. So we're going to go cos of 60 degrees is equal to, can you see this? I hope so. Cos of 60 degrees is equal to adjacent, which is y, over hypotenuse, which is 7. Okay? So the whole purpose, everything that you need to do right now is get y by itself. And the way you do this is you cross multiply this up. Now before you cross multiply, in your calculator, you're going to punch in cos 60 degrees. Let me get my calculator and find out what this is. Later on, later on, when you continue with mathematics in grade 12, you're actually going to know what this is because there are special triangles that give you information that are set and you know automatically what this is, okay? So what you're going to do with your calculator, you're going to go 60 and you're just going to go straight up cos. And that gives you 0.5. So cos of 60 degrees is 0.5. So what you have here right now is, let's actually do this. So this becomes 0.5, are we on the board? We're on the screen. 0.5 is equal to y over 7, right? Now what you're going to do is cross multiply the 7 up. So I'm just going to go over here. You're going to have y is equal to 0.5 times 7. So y is going to be equal to 0.5 times 7 and that's equal to 3.5. So y, the answer for y is 3.5, okay? Now we need to find x, how are we going to find x? Well, I'm going to erase some of this stuff, okay?