 This video is called Right Triangle Trig 2. So again, we're just doing some practice problems. This one's just a little bit different, so pay attention. Follow what I do, take good notes, and I think you'll be just fine. For this problem, we're told that we have a triangle PQR that has a right angle R, and they tell us that little P equals 80, little Q equals 60, and little R equals 100. I'll tell you what that means in a minute. The first thing we're told to do is to draw the triangle and label its sides. So find just a little bit of room on the right side of this problem. We know it's a right triangle, because they tell us right angle is R. Now, they don't tell us which vertex is Q and which is, well, what's the other letter, P, so we can pick. I'm gonna put P on the top, Q on the bottom. Now, what do they mean about these little letters? Well, small P is the side opposite angle P. The small Q is the side opposite angle Q, and side R is opposite angle R. So they tell us that small P is 80, small Q is 60, and small R is 100. So that is drawing and labeling the sides. Then it says to write the ratio, which would be the fraction, and the decimal value to the nearest hundredth for each. All right, so cosine of P. Well, I still have my Sokotoa, so I don't have to memorize anything. I just have to know where to look. The cosine is adjacent over hypotenuse, and we're gonna go from the perspective of angle P. So from this perspective of angle P, well, let's think about what do we have? The hypotenuse is always gonna be the hypotenuse. This would be the opposite, and Q would be the adjacent. So adjacent over hypotenuse is going to be 60 over 100. Now, you certainly could reduce that to six over 10, or you could reduce that to three over five. I personally, this is Mrs. Milton, would accept any of those ratios, because it didn't say in the simplest form, but you'll wanna ask your teacher which ratio they would prefer. Then the decimal value, hopefully you have your calculator handy, you'll just do, you'll punch in three divided by five, and it gives you 0.6. So the ratio is your fractions, and then the decimal value, and since it says to the nearest hundredth, technically we should say 0.60. All right, now let's go ahead and answer question 15, which is asking for the tangent from the perspective of Q. So we're changing what perspective we're looking from. Now we're looking from Q, so I have to relabel. Well, the hypotenuse will stay the hypotenuse, but now side P becomes my adjacent, and side Q becomes my opposite. To find the tangent, I look up at Sokotoa, and remember tangent is opposite over adjacent. So from the perspective of Q, opposite is 60, and adjacent is 80, so that would be my ratio, you certainly could reduce that to six over eight, or to three over four, and then when you punch that in a calculator, Q becomes 0.75. So the ratio is the fraction, and then the decimal to the nearest hundredth is the 0.75. So again, you're just getting practice on looking at right triangles, labeling them correctly, and answering things about it, and getting used to the vocab of cosine, sine, and tangent.