 More triangle before we move on to some of the aspects of trigonometry or geometry, okay? Here, we've got another triangle. I've given you two sides. This time I've given you decimals, which is whatever. It doesn't make a difference. It can give you any type of number. It can give you numbers with 10 decimal places at the end of it. You use the same operations. And we've got Sokotoa and A squared plus B squared equals C squared, which is the Pythagorean theorem. So, again, we're going to have to decide which one of these we want to solve first. Now, again, the question is going to be solve. What they're going to ask you to do is say solve. Sometimes they won't even ask you to solve for the whole thing. They'll just say, oh, solve for theta, solve for beta, or solve for a side, okay? But right now, just to cover all aspects, we're going to solve everything. So let's say we want to solve for beta this time first. So first thing you're going to do is think about Sokotoa and put yourself on this angle. So if you're sitting here, which pieces of information do you have from a triangle? And that's what you have to be thinking about. So if you're sitting at beta, you have the hypotenuse, which is across from the 90 degrees. And you have the adjacent, which is 4.1. Now, those are the only two sides you have, and you're missing the opposite. So you can't use sine because sine has an opposite of an angle. And you can't use tan because tan has the opposite. So you're limited to using the cosine. So what you're going to say is the cosine of B is equal to adjacent over hypotenuse. So cos, the formula is cos theta is equal to adjacent. I'm going to spell this correctly. Adjacent over hypotenuse. Now theta is a general term. I'm not talking about this theta. I'm just saying theta, which is a general term for an angle. If you're actually solving for theta, you would say you couldn't use cosine because you don't have the adjacent here. So just so you don't get thrown off here, I'm going to change this theta to the angle that we're actually solving, which is beta. So cos theta is equal to adjacent over hypotenuse. We're looking for beta. We don't have it. So that stays where it is. We have the adjacent, which is 4.1. And we have the hypotenuse, which is 6.2. So we're going to go cos theta is equal to 4.1 over 6.2. Now these are fractions or decimals. Now decimals, these kinds of numbers, don't worry about trying to do it manually. You can just use your calculator. So 4.1 divided by 6.2 is 0.666, 0.6612. So this becomes cos beta is equal to 0.661290, blah, blah, blah. Now when you're solving for these, do not round this up right away. What you want to do is round your answers at the end because if you round too early, it's going to throw your sick figs off and you're going to get the incorrect answer. So always take this up to whenever you're doing this kind of division. Always take this up to 5 or 6 decimal places just to make sure you're getting the right answer. So what you're going to do now is you want to get beta by itself. So beta is going to be equal to, and if you remember from last time, the only way to separate these, this doesn't mean cos times beta. You do not divide by cos to get beta by itself. You grab this, bring it over to the other side and the only way to do that is to take the inverse cos of it of 0.66129 and this is just a function on your calculator. All you're going to do is go second and it's usually you got cos and then you have cos inverse above it so you have to kick your calculator function up one and it becomes inverse cos of that, which is 48.60 degrees. Keep this in one decimal place. Because they gave you one decimal places in the question, you keep the answer to one decimal place. Sort of sick fig consistency. So beta is 48.6 degrees. Now since we have this angle and we have this angle, we know the sum of all of the angles in a triangle is 180 degrees. So all you do, you say 180 minus 90, so you took this away, which gives you 90, minus 48.6 is equal to 41.4 degrees. So right away by doing one operation and knowing the relationship in a triangle, which the sum of the angles is 180, you can get the second answer. So if this question was worth three marks, you already got two marks out of it. How are you going to solve for W? You can use a Pythagorean theorem, which would be a squared plus b squared equals c squared. Now c is always the hypotenuse and this could be a or this could be a. You could make a difference, you could switch them up or you could use Sokotoa. Now let's decide to use Sokotoa because last time we used a Pythagorean theorem just to show you how this works. What I'm going to do is I'm going to erase this. What we did here, so give us some room to do the problem. You can just pause the thing if you want to film, just if you want to copy this down. Let's decide which angle we're going to use to figure out what W is. It's up to you because we have these guys, you can use both angles, you can use sine, cosine or tangent really. Let's use sine and you know what? We're going to use two of them just to convince us off that it doesn't make a difference which one you use. You're going to get the same answer. So let's say we want to solve for W and we're going to use angle theta, which is 41.4 degrees. So we're going to put ourselves here we're at 41.4 degrees. What's W relative to 41.4? Well that's the adjacent. So we have adjacent. Now we're not going to use this one because we chose to use this angle because that's opposite over hypotenuse that would be this over this. So we can use cosine and tangent has adjacent as well. So we're going to use both these things. So we're going to go cos theta is equal to adjacent over hypotenuse. So theta we already know which is cos 41.4 is equal to adjacent which is W over hypotenuse which is 6.2. So what you're going to do is you're going to go cos 41 you're going to go 41.4 and you're going to take the cos of it because that's what that means. That's going to give you 0.75 is equal to, well there's zeros here let's use complete same things 0.5011 is equal to W over 6.2 and the way you get W by itself now you cross multiply this sucker up. So you go 0.75011 times 6.2 and that gives you W is equal to 4.65069. Now you don't need this many 6-fig because they only gave you one 6-fig in the question so you can kick this down to 4.7. So all of a sudden we've got 4.7 for W and we solved this triangle. Now what we're going to do is we're going to use 10 to solve for the same W again just to convince ourselves we're going to get the same answer.