 So questions from the homework any of these you want me to go over now is your chance to ask Yes Okay, so no, I'm hoping oh clicky-pen. Thank you I'm hoping number two where you have the triangle started to get pretty boring. That's my almost my goal It you'd be like jays. Mr. Duke. It's opposite. It's a jays. That's a pie and walk through it The word problems are the tricky ones. So sorry here, which one three what three be on a sunny day The Sun's rays strike the ground at an angle of 53 degrees a tree There's my tree So as good as art as you'll ever see with me 50 sorry 18 meters in the height So I think this right here is 18. Yes Casts a shadow There's a shadow Here's the Sun's rays Says strikes the ground at an angle of 53 degrees. So I'm pretty sure it's that I know not to put it up here because it did say strike the ground them clever it up And I know this one's 90. So that's not 53 degrees Okay, here's the question Kiera if you're measuring the length of a shadow, how do you measure the length of a shadow? And I think the answer is kiddo you measure it on the ground. That's X Did you get that far so far? Okay, that makes sense. I tried to explain to you how my brain approaches. I mean, I'm hoping you can all draw the tree Maybe not But hopefully and then when it says height, I hope you clue in height as a vertical Then it's more interpretive. Oh, no with the ground better put the angle down there By the way, then if that's my angle opposite of Jason to hypotenuse How about here? Which trig function? Yeah What always goes next to the trig function and don't say the degrees because that's never what I said What always goes next the angle because sometimes it's a variable, but this time we know it 53 equals what over what? 18 Over X the X is on the bottom when you cross multiply you'll then have to divide on your next step as well Is that okay though? Any others? DEF and J went okay We talked about angle of elevation and angle of depression And I told you that I actually remember it that way depression and why do I remember that way Tanner? Because when I say depression automatically my eyes lower. Oh, yeah, it's this angle, right? It's a dumb way to remember but it works for me, right? Okay, can then later on today if you'd be so kind as to hand that in we'll move on to today's lesson fairly short So lesson four call my friend. Can you read to me the title? What this really means is now I can ask you to find anything given anything sides Angles and I say find every missing thing of a triangle. That's what we mean by solving a triangle You need two pieces of information You either need two sides and then you can use Pythagoras to find the third side and you can use the shift button shift coast shift hand shift Sign to find the angle or you'd one side and one angle so today it says We'll combine the last couple of topics order to solve word problems and triangles using three tools of trigonometry Each of the following tools requires that you know different things about a triangle. You're trying to solve The first one is the Pythagorean theorem. We call that a squared Plus b squared Equals c squared. Will I give this to you on your formula sheet for this test? Yes, if you're having to look it up though, that's my indication that probably you haven't done the homework With this tool you're using it to find a Missing side Because you'll notice there's no angle in here. What was the variable David? Do you remember I like to use for finding an angle that Greek letter. Do you remember it? Theta, okay, no theta in here means you're finding a side You must have Two sides in order to use this If you have the hypotenuse Zach, make sure you put the hypotenuse here Always goes where the C is that was the only thing you have to remember and then how to get rid of a squared square The second tool we gave you was the primary trig ratios and we had a handy-dandy acronym for that. It was so Oh tour With this tool you're using it to find a side or An angle and you must have Adrian I'm gonna use some abbreviations from the geometry unit. You must have Two sides can I write that as ss remember our congruency rules or? What do you think s a stands for one side and what Emma One angle and the 90-degree one you need that one too because it does say at the very top here solving right angle triangles If they don't give you that all the rules are off, okay? And then the third one is a lovely review from last year This is why we do geometry before we do trig if we can the angle some of a triangle Rob, what was the angle some of a triangle every triangle's angles added to what we use this to find Can I abbreviate angles with an angle symbol and an apostrophe s You need Two angles and then you can go 180 minus the two to find the third one We do have an important note Nicole the first two tools Pythagoras and Sokotoa can only be used when you have a right angle triangle and We are in one two or three lessons Nicky gonna start to look at non-right angle triangle And that's where the new stuff begins where to learn something called the sine law and the cosine law also useful especially in physics But a little bit trickier Example one Alicia it says Alyssa it says good gosh. I don't know why I'm having so much trouble with your name Come stupid The mind goes first and then you know the hair is next right? For each of the following find all the missing sides and angles what I'm gonna say on your test is Completely solve this triangle means Rachel find anything that's missing. Okay What's the first thing Rachel it wants us to find do we have enough information here to find angle M? Yeah Zack how big is this angle right here? 90 that's a little symbol right how big is that? Can you in your head find how big angle M has to be or use a calculator? We're using angle sum of triangles right by the way, is that you want the shortcut since this is 90 It's really these two add to 90 because 180 minus 90 is 90, so it's 90 minus 62 28 am I right calling what's the next thing it wants me to find? MD which is That one here's the angle that they gave me Opposite adjacent or hypotenuse this 15 opposite Adjacent or hypotenuse this X Hypotenuse which trig function is oh, I agree with you Joel and Joel what always goes next to the trig function? The angle what is the angle this time? 62 and sign is what over what well the so in so katoa stood for Opposite over hypotenuse Joel in this triangle or specifically what over what? Nice good solve for X I'll do it up here. Let's see if we get the same thing Better make sure that I'm in degrees You get 16.99 Did it say what to round off to in the question? No, then I'll go to two decimal places. That's my fallback. So I'll go 16.99 Did you try the sign of 30 earlier in class? I got 16.99 Nikki, what's the next thing they want me to find? Udd now you have a choice Since I know this is 16.99 now. I know two sides and I could use Pythagoras Go ahead I'm gonna use trig and the reason is I don't want to use this one unless I have to because if I made a Mistake on this I'll be using a mistake to find another answer. Well, I get other answer, right? No, so I'm gonna choose to use trig again. You're ready Here's my angle. Here's what they're asking me to find. I'll put a Y there since I used an X already Nikki opposite adjacent to hypotenuse adjacent to hypotenuse Which trig function uses those two what always goes right next to the trig function? Equals what over what kiddo? Yep. Good. Let's solve for Y 7.98. Yeah Okay Make sure you're practicing on your calculator So Joel, let's suppose I finished the test and I had a question like this here so I can check my answer Pythagoras should also work. I should also be able to go 15 squared plus this side 7.98 squared equals and when I square root that number Do I get 16.99? I got another way to check. I'm right. So the first kind of question that you're gonna get in the homework Tanner is One angle and one side saw second kind of question you're gonna get is two sides Okay, Rob, what's the first thing it wants me to find? No, what's the first thing it wants me to find angle D? Hmm Can I find angle D right now using angle sum of triangles? No, because I don't know that one either Okay Now we're gonna have to use trig so katoa to find angle D Kayla This 12 opposite adjacent or hypotenuse. I totally agree How about the 13 I totally agree which trig function is oh Sin is when you swear in my class or when you're late and don't do the homework Sign and Kayla what always goes next to the trig function and what's the angle this time? You know what instead of an X. How about I put a D because that will help me keep things organized Equals what over what? Okay, am I gonna cross multiply here What am I gonna do then? Ah? Yeah, this is where we went and again those you with your calicators better practice second function sign bracket 12 divided by 13 Close bracket when I hit equals or enter this should tell me the angle that it came from what angle did it come from? I'll go sixty seven point four You know what I'll go sixty seven point three eight. I'll go to two decimal places and be uber accurate Sixty seven point three eight degrees Well, you get that okay You lying did you try it you got a new calculator better practice saying? Adrian what we get here? And how big is this angle you have to know this how big is this angle yeah It is you know how I know because they put that little symbol right there look down at your piece of paper in front of you Okay, there's a reason why I photocopy this it so you can actually see it in front of you. So ready how big How big angle D Okay, how big is angle low? How can we find it? I don't know how do we find it? Just wrote a test on it kiddo Sam. How do I find it? Oh? Angle sum of triangles 180 minus so you're saying 180 minus 90 my not times minus sixty seven point three eight how big is angle oh? Twenty two point six two I'd be fine with that on a quiz or a test because they didn't tell me how accurate to go I'm being uber accurate just in case I use this to find other stuff, too Just so we know what we did How about Nikki in our notes? We write angle o equals a hundred eighty minus ninety minus sixty seven point three eight So that when you're studying later on you know what the heck we did Tatiana. What's the last thing it wants me to find? Okay, let's put our x right there Now we can use so katoa or we can use Pythagoras I'm gonna choose to use Pythagoras because Nikki if I use so katoa I have to use this angle or This angle and I might have got one of these wrong I know the 12 and the 13 are right because Joel they gave me those in the diagram Right do you always just twitch your eyebrows at a blank door? That's your move is it ladies be afraid so Joel I'm gonna choose to use Pythagoras I'm gonna write here a Squared plus b squared Equals c squared am I trying to find the hypotenuse or did I know that or do I know the hypotenuse? What is the hypotenuse and that always goes where the c is? right and I said a and b doesn't matter what order you put them in I like the x to show up first I'm gonna go x squared Plus 12 squared Alexis, how will I move this 12 squared over? Subtract now by the way, it's not gonna be 13 take away 12 is one. It's 13 squared take away 12 squared I'm gonna go minus 12 squared from both sides and on your calculator What is 13 squared take away 12 squared? I? Think 25 if I'm doing the math right in my head Yep, Jacob how to get rid of a squared. What is the square to 25 in your head Jacob Rob? Is he alive? He is okay Tanner you're pretty good in my prime in university Tanner I could actually go like this so my prop couldn't see my eyes and I could move my pen in my sleep So it looked like I was taking notes Not as hard as you think of course the other options just bring some caffeine and sleep when you Nothing got Colleen a little bit there turn the page Cole this is the last question told you be a short lesson. I haven't forgotten word problem Okay, no problem Hey, by the way, what shape is gonna appear in this word problem somewhere Rachel? What do you think? Gonna be a triangle okay, and if they mention a cliff. Let's assume cliffs are vertical Read to me Rachel. There's my cliff Here's the person Does that make sense so far Kiera? This is how I put these together. Oh, was there a number attached to the cliff? Hey, let's put that right here Keep reading Rachel fires Okay, so apparently there's a ship out here somewhere There's my ship Looks like an umbrella shut up. Oh, oh Where would this 800 go on the slanty part? Or on the bottom part It says 800 meters offshore. Where do you think would make more sense? bottom 800 oh And we said we'll assume cliffs are vertical so we know we will assume. It's a 90 degree angle right there. Yes Keep reading Find except here's what I like to do. I'd like you to read it like this find the angle of depression of the cannon Go ahead. I know you want to come on find the angle of depression Okay, and why am I doing that because here's the angle we're talking about Rachel They want me to find that angle theta Right, how do I remember that angle of depression? Oh, yeah, this one from my eyes down, right? Here's the problem That angle is not in the triangle Ah anybody see it what Alternate interior there's a z so I can find that angle by finding that one Okay Joel Opposite adjacent or hypotenuse based on that angle there I totally agree. How about this? I totally agree. Did you all turn the page or are you on the same page? Okay, I've turned the page so I have to write so uh So hey, what's trig function joel tanner what always goes next to the trig function And what's the angle this time? Theta, thank you for remembering the greek word. I knew I could count on you tanner equals what over what? Good find the angle. Oh, how do I find an angle? Am I cross multiplying here? I say no, no. In fact, it's going to be all calculator This is why I've been yelling at you to bring the same calculator over and over and you need to know how your calculator works I Not help you figure it out on a quiz or a test folks Adrienne, what'd you get for your angle? Since I saw you finally start to type 9.2298862 is that right? Yep Let's go 9.23 degrees Which means by the way my scale here is terrible, but I don't care tanner a nine degree angle would really look about like that Like almost like nothing at all barely at whatever Rachel keep reading after the word then comma then what? Which of these lines do you think would represent the distance that the cannonball traveled? Well, let's be clever They gave me that they gave me that I doubt they're asking me to tell them that you know what I'm pretty sure the x is going to go Right there Am I going to use so katoa here or pythagoras? To find the missing side I'm going to use pythagoras. I could use so katoa assuming. I've got this 9.23 right, but why risk it I would use it to check my answer later on tanner before I hand the quiz there if I got the same answer both ways I don't know. I'm right. That's a nice feeling Pythagoras says Okay Cole this x is if the hypotenuse or not Oh, so it's going to go by itself And it's going to be 130 squared plus 800 Square you'll notice i'm not writing a squared plus b squared equal c squared We're going straight to plug in a number if you feel comfortable doing that go ahead Is the x squared by itself already joe? Then can you go to your calculator 130 squared plus 800 squared and then when you're done that and press equals How to get rid of a squared? Yes, I hear the phone vibrating whoever that is but it's un-vibrate. It's not timbits Although you could turn it off and be out of contact with the world for 35 minutes Kayla would you get 800 by the way look up There is a built-in error check What's the longest side you know 800? This side here is longer or shorter than 800 It's got to be in other words if you get an answer less than 800 You probably subtracted or put the x on the wrong plate like let's clue in and look at our diagrams and say Well, I can't be right or can you get a negative answer? If you got a negative you've screwed up. So one of the things I like about trig There is chelse a bunch of built-in error checks. Sorry, what'd you get? 810 anybody else? Yeah 810 meters What's your homework? It's nice out by the way So hopefully you won't have any you're gonna get lots of time First of all if you haven't completed lesson one or two or three those get those done and caught up today. This is it By the way, Wednesday, what do you guys have? So this if you play this right means no homework for the pro d-day, right? number one I encourage you in number one to get as fast as you can And if you need to show if you can get away with showing less work Go ahead Now Joel that means you can just copy the answers from the back. I'm going to assume you're not that's Careless, right? number two number three skeg number four Oh, why don't you just say all of it mr. Dewick? Because I think you can expect a take-home quiz on so katoa either on friday or on monday of next week Okay, then we move into the newer stuff right click