this video looks at using the so cartoa equations to find missing sides when we know one angle and one side now the first step is always to identify which signs are involved which one is the unknown and which one is the known now in the first one the 13 is the hypotenuse it's opposite the right angle the unknown is opposite the angle so that's called the opposite and we then identify which of the equations uses opposite and hypotenuse when it's the sine equation so sine now the X here in the Equator the angle not the X in the question so sine of the angle in this case 42 is equal to opposite which is X over hypotenuse which is 13. so to find X I need to rearrange this equation by timesing by 13. so x equals 13 lots of sine 42. so I input that into my calculator as I see it 13 times sine of 42 and I get 8.7 so X has a length of 8.7 okay the second one we have a known and an unknown now the unknown Y is opposite the angle so that's the opposite whereas the 10 it's not hypotenuse it is next to the angle it is the adjacent so again adjacent opposite is tan So Tan of the angle 37 equals opposite y over the adjacent so again to find Y and let's rearrange the equation by times in by 10 so Y is 10 lots of tan 37 so I input that into my calculator 10 lots of tan of 37 and the answer is 7.5 so y has a length of 7.5 now then the third one angle Known Unknown the unknown is opposite the right angle that is the hypotenuse this site here is next to the angle it is the adjacent so adjacent hypotenuse is cos so COS of the angle which is 41 in this case is the adjacent 13 over Q which is the hypotenuse now then this is a bit different to the first two equations because the unknown is now below the equation so to rearrange this request two steps I first of all times up by Q so Q lots of cos 41 is equal to 13 of times by Q like at times by 10 and 13 here so to find q i now divide by COS of 41. so Q is 13 divided by COS of 41. if I input that into my calculator so 13 divided by a COS of 41 and I get 17.2 so Q has a length of 17.2 skills how to identify the two sides in the question to write down the equation and then to solve it either using the one step method when we want the known on top of the equation or the two-step method when the unknown is beneath the equation but it's so Cloud finding sides this video talks through how to find missing angles when you know two sides now then the first step is to label the sides either opposite adjacent or hypotenuse now the hypotenuse is always the longest side opposite the right angle so hypotenuse hypotenuse hypotenuse from the first triangle that's not given but we give them the side opposite the angle so that's the opposite and we know the other side which is next to the angle that's called the adjacent right then we then identify which of the so car TOA equations to use now we know the opposite and the adjacent so we use the tan equation So Tan of X is equal to opposite over adjacent opposite over adjacent or five twelfths then to find out X we have to do the inverse tangent function or shift Tan on the calculator or inverse tan so it's inverse tan of 5 12. so we put that into our calculator and we get the answer which is 22.6 degrees but the second question we know two different sides here's our angle one of them is the hypotenuse because it's opposite the right angle this one here is not opposite the angle it's therefore the adjacent so we know the adjacent and hypotenuse so we identify which of the equations uses those two sides it's the COS ratio so COS of X is equal to adjacent over hypotenuse adjacent over hypotenuse so four thirteens so to find X we do the inverse cos of 4 over 13. so we put that into our calculator inverse COS of 4 divided by 13 and we get 72.1 degrees so the final one here's our angle now that one there is the hypotenuse and this side is opposite the angle so that's the opposite so opposite hypotenuse it's the sine equation so sine of x equals opposite over hypotenuse find X would be inverse sine of five over ten or a half so we get x equals 30 degrees so there we go that is how to use sine cos and tan to find missing angles