Trigonometry Lesson 7 "Trigonometry Problems"

hi welcome to the trig unit lesson s solving problems with trig okay basically this lesson is mixing up the problems you've learned so far so let's jump in and get moving you should know everything now it's just putting it mixing it up and deciding which which strategy do I use okay so let's go through and write our ratios the more you write them the more you'll learn them so the sign is our opposite over our hypotenuse or so cosine is adjacent over hypotenuse or K and then tangent is our opposite over our adjacent or TOA so we have SOA TOA so use that as your reference as we go through through these problems okay now we're going to jump down here and start running through the problems and you're going to ask yourselves these questions right here is this a forward problem or a backwards forward when you're looking for a side backwards when you're looking for an angle which sides do I have to reference or which sides am I looking for once you know that then you can decide which trig function am I going to use depending on which sides I have then we're going to set up and solve each of these problems so let's start with this first one here okay we have a 90° angle here a side x 56 and then an angle that measures 37° okay is this a forward or a backwards problem hopefully you said forward because we have the angle when you have the angle it's a forward problem okay which two sides are we dealing with I always like to label my opposite first then my adjacent leg and then my hypotenuse so I'm not using hypotenuse on this one so I'm using opposite adjacent which one is opposite adjacent tangent so I'm going to take the tangent of the angle and the angle given 37° is equal to the ratio of opposite over adjacent so my X is on top because it's opposite and adjacent is on the bottom because it's given okay now let's talk about how whoops slide this over there we go so you guys can see it now we got we've got to solve it okay so if you remember when we're working forward we actually have to change that tangent 37 uh well let's stick a one under it first and then we're going to do a cross product so let's change that tangent of 37 to a decimal so I'm going to just go forward and take the tangent of 37° and I close my bracket and I get 7536 so 7536 all over one and now I'm going to work my cross product so when the variable's on top is a little easier cuz x * 1 is just X and then 7536 * 56 is 41.2 so I'm going to get 40 or 42.2 excuse me 42.2 and that's how long this side is over here and there you go and that's how you find that missing side okay so there's our first one and that was a forward problem because we were given the angle let's look at the second one okay on this one we're given an angle of 90 up here an X here 18 and 22 okay we do not know the angle so this is going to be what a forward or a backwards problem hopefully you said a backwards problem CU we don't know the angle so we're going to have to work this one backwards or use our inverse button right that X to the1 or or s to the 1 cosine or tangent okay so which two sides do we have from the angle of reference we have the opposite this is the adjacent and this one's the hypotenuse okay we're not using the adjacent so which one uses opposite hypotenuse go back if you don't know your trig functions opposite hypotenuse is sign so we're going to use a sign the sign of what angle well we don't know it so that's our X is equal to the opposite which is 18 over the hypotenuse which is 22 okay now since we're going backwards we're going to have to use that inverse button so I'm going to do the second s to get X or S to the1 of 18 over 22 so let's type that in clear out here I'm going to zoom out just a little bit to help you guys zoom out there we go that helps a little bit makes my screen a little bigger there we go okay second and sign of 18 ided by 22 and that angle is what 35° right 34.9 would round to 35 so X I'm sorry 55° so it's 54.9 or 55° so that means this angle right here is 55 but just thinking through do you remember how do you find this other angle well we know that two acute angles add to 90 so we can take 90 minus 55 and know that this angle over here is 35 we weren't asked to find that but just remember that's how you do find that one okay so let's look at the next page we've got two more problems see if we can find these missing parts here forward or backwards that's what you need to be asking asking yourself okay you've got an angle of 44° here an angle of 90 here an X and a 66 since you have the angle of reference this is going to be a forward problem so you're not going to use your second function key you just use the regular trig s cosine or tangent which two sides okay opposite we're not using we are using adjacent and hypotenuse okay which one is adjacent hypotenuse go back ad Jason hypotenuse is cosine so we're going to take the cosine of 44 and that's equal to the adjacent which is our unknown X over our hypotenuse which is 66 now let's do some calculator stuff let's take your cosine of 44 over 1 so grab your calculator cosine of 44 and it is 71 93 7193 over 1 = X over 66 do my cross product so I'll just take that answer times 66 and I get 47 so X is 47 and that's 47 but I'm looking at the tenths and the tenth does not round up so that's just 47° so I'm sorry 47 this is not an angle it's a measurement so it's just 407 okay that's how you'd work that one so that one was a forward problem okay let's look at the fourth one here and see if we're missing an angle or are we missing a side okay on this one I'm just going to zoom this one in try this one on paper here it's my last one there we go okay I've got my reference angle here and I don't know the angle so is this a forward or a backward this one is a backward problem we're looking for the angle okay so which two sides are we using this one is the opposite we're not using it so which trig function uses adjacent hypotenuse hopefully you're getting more comfortable with that the answer is cosine cosine of our unknown angle X equals the adjacent oops I've got those labeled wrong don't I this one's hypotenuse this one's adjacent okay so let's rewrite let's make sure we set the ratio up right uh adjacent is 71 and hypotenuse is 79 and I think I would have noticed that because we know that the hypotenuse is always the longest okay so now we work backwards we work back WS so let's take our handy dandy calculator boy we're zoomed in way too far here there we go okay so let's clear and take the second function second function cosine to get our inverse of 71 / 79 and the answer answer is 26° so X is 26 okay had you had I done it wrong and put the 79 over 71 it actually would have come up with an error because cosine can't of the ratio of cosine can't be greater than one so it would have given me an error anyway okay so those are four practice problems now what you're going to do is you're going to try this one okay couple leading questions which sides do you have which trig function are you going to use set up and solve it since this is an inverse uh section you may want to look decide is this an forward or a backwards problem figure out which one you're going to do before you start and that kind of helps you out so the answer will be in the course so good luck and I hope this video helped