does the sohcahtoa acronym refer to well s stands for sign C stands for cosine and the T here stands for tangent okay so what the sine is it's a ratio and the ratio is where you're comparing two things as a fraction so what we're going to do is we're going to take the sine of an angle and what it equals it's the opposite side over the hypotenuse so this acronym helps you because it's going to be the second letter divided by the third so the opposite side over the hypotenuse the cosine of an angle is the adjacent side over the hypotenuse so you can see a over H and then the tangent of an angle equals the opposite side over the adjacent side so you can see second over third over a so these are called trigonometric ratios and this is for right triangles and I'll show you some examples here so say we have this right triangle ABC and we want to find the sine of angle a so what that means is it's the opposite side over hypotenuse C over H and so if we're standing here so we kind of have this perspective like you're at this vertex this angle here the opposite side you go across diagonally so that's going to be five okay the hypotenuse is the side that's across from the right angle okay so that's 13 so the sine of angle a the ratio of the two sides the opposite and the hypotenuse is 5 thirteenth's okay now if we want to find the cosine of angle a you can see we're going to do the adjacent side over the hypotenuse okay now adjacent means next to okay so if you're here adjacent means next to that's this side and this side we want to use the 12 not the 13 the 13 is the hypotenuse is to cross from the right angle that's the longest side so when they say adjacent don't pick the hypotenuse pick the other one okay so that's going to be 12 divided by the hypotenuse adjacent over hypotenuse so that's going to be 13 okay now the tangent of angle a to let this angle tangent is opposite over adjacent okay so if you're here offices across adjacent is next to so that's going to be five twelfths okay so far so good okay now let's go over here to this angle okay angle B so we're changing our perspective we're at this vertex so the sine of angle B is opposite okay so we're going across so opposite which is 12 over the hypotenuse which is 13 okay the cosine of angle B is adjacent so you can see here Jason is next to five over the hypotenuse 13 five 13 and the tangent of angle B is the opposite side over the adjacent side okay so that's gonna be 12 over 5 okay so this is how you find the sine cosine and tangent in a right triangle we only use the two acute angles we don't use the right angle so there's no sign of angle C okay or cosine or tangent okay just the two acute angles not the right angle okay so let me show you how you use these trig ratios in solving problems so over here we have a right triangle you can see the forty degree angle and we want to solve for this missing side here X so we have to ask ourselves as what trig function ties together this single this side and this side okay well let's see if you're at this angle this is the opposite side and this is the adjacent side to this angle so we go to our acronym so Toa and you can see opposite and adjacent that's the tangent ratio so that's what we're going to use so we've got the tangent of 40 degrees equals the opposite over adjacent 5 divided by X now you can cross multiply okay anything divided by 1 is itself so you can cross multiply and you get x times the tangent of 40 equals 5 times 1 which is 5 then all you have to do is divide by the tangent of 40 okay on both sides and this is an exact answer you can do that on your calculator and you're gonna get the length of this side now one quick hint something that helps is that you can switch these on the diagonal okay when you have a proportion like this or ratio you the ratio you can actually switch these so I could have saved myself a little bit of time by putting X here and tangent of 40 here and I would have had it in one step okay let's go to the next one so here you can see another right triangle we've got 35 degrees and we want to figure out what trig function ties together the adjacent side and the hypotenuse suits across from the right angle that's the hypotenuse adjacent is next to so that looks like cosine ties together adjacent and hypotenuse so we've got the cosine of 35 degrees equals it's always going to be the second letter over the third letter and that acronym so x over 8 and then what you can do is you can cross multiply x times 1 is X 8 times cosine of 35 and now you're ready to put that in your calculator and get the length of this missing side okay last example I'll show you here is a now we've got this angle 50 degrees and we're trying to tie together the opposite side so you across and the hypotenuse across from the right angle so that's going to be let's see opposite and hypotenuse you can see that's going to be sine Soh so right so sine of 50 degrees equals 4 divided by Y I'm going to use that little technique I was showing you earlier about switching these on the diagonal okay so Y over 1 equals 4 divided by the sine of 50 degrees and this is an exact answer it's ready to be put in your calculator and you can get a decimal approximation for the missing side so this is how you work with right triangle trigger a she owes and if you enjoy these videos go ahead and subscribe to the channel and I look forward to seeing in the next video