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7.1 & 7.2 Notes

Added Jan 21, 2015 •

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okay guys remember is you doing this you can pause rewind replay if you have any questions just make a note within your notes and you can ask me when you the class okay we're starting chapter 7 it's all about right triangles so the first thing we're going to do is Pythagorean theorem you should be familiar with that and the parts of a right triangle but just to remember that the side that is always opposite of the 90 degree angle is your hypotenuse and remember that the hypotenuse is always the longest side  counts awesome the two sides that the 90° angle are your legs so this is a leg and this is a leg and remember that the Pythagorean theorem was a squared B squared equals c squared and remember that she is always the hypotenuse so C is always your longest side and beer your next it doesn't matter which one is a or which one is be  now remember that it only works for right triangles it will not work for any other What triangle only right triangles right triangles are the only one that's has a hypotenuse and remember you use the Pythagorean theorem to find us does a right triangle when you already know two sides it won't work otherwise and remember C is always the hypotenuse okay so next we have a couple of examples look at example one you'll see that you know the two legs but you have to find my partner's now that's the first thing you should always do identify which side is the hypotenuse and label it C so this will be our a this will be our be for vice versa so if it's a squared that will be three squared plus b squared that will be 7 squared equals c squared which will x squared now just do your algebra 9 + 49 equals x squared 9 + 49 58 equals x squared I remember to find the square root of each side because the square root cancels out of square what if you're keeping it in radical form you'll have x equals the square root of 5858 does not have a factor that is a Square now if you were to type it in your calculator and get the decimal it would be 7.62 okay over here this is our so this will be a and b so if I do a squared I will have x squared plus b squared 6 squared c squared is 6 32 now that whole thing is squares wood has to look like that and remember about what we talked in class you have to square the six and you have to where the square root of 2 so when you square the six you get 36 and when you square the square root of 2 the square in the square root cancel out and you just get what's left underneath so you're 36 x - which is 72  King how long have x squared + 36 now subtract 36 you can get the x squared by itself that cancels x squared equals 36 take the square root of each side and the square root of 36 is a perfect square so it's x equals 6 so this side is 6 now look at this trapezoid in C  it says fun the height the height remember is always the perpendicular what you're trying to find is right there that's going to be your ex now if you notice these two are marked equal and 20 is actually this holy that's not Mark real well but it will be better in your homework okay so if this part from here to here is 12 that leaves eight for the ends 8/2 is 4 so that would make this part for this part for and that part 12 so use not right triangle right there see will be your 10 your legs will be x + 4 so you would have x squared 4 squared equals 10 squared that will be x squared plus 16 equals 100 subtract the 16 from both sides that cancels x squared equals 84 now take the square root of both sides smell 84 does have a perfect square in it and it is 484 is for x 21 so you can take the square root of 4 that stew and the 21 has to stay underneath cuz it does not have a park switch going to √ 21 if you put it in decimal form that's 9.17  took a look at me now D is a square all the sides are marked equal and it has a diagonal that it's the five the square root of 2 so one of these half makes a perfect right triangle and we need to find the leg they would be more both with an ex because they're exactly the same so that's your a in your B5 √ 2 is your seat so a squared would be x squared B play would be x squared equals 5 the square root of 2 squared plus x squared is just like x + x it's going to be do x square equals that remember Square the five that's 25 Square √ 2 they cancel you get what's underneath 25 * 2 is 50  divide both sides by 2 to get rid of that and get x squared by itself a squared equals 25 take the square root of both sides perfect square is 5 turn the next page remembering an equilateral triangle and from the vertex angle in an isosceles triangle the median and altitude are the same mine so remember in the equilateral triangles when we did that when we drew the altitude which was straight down perpendicular it so cut that side in half so the meeting in the altitude where the same remember it was also true from an isosceles but only from this vertex angle up there that what's the weather say that's going to come in handy so like an example to it says find the area of an isosceles triangle with side length of 20 inches base of 24 side length of 20 its isosceles so both of the top sides  will be 20 those will be our too what are equal the base is 24K now it says find the area what area equals one half base times height okay so our base of course is 24 so we have 1/2 24 x our height the problem is we got a fun height no remember the height is the altitude so it's at perpendicular line and we don't know it so we have to find it but we can is a right triangle and find it so if we use this right triangle right here we can find the height now if the base is to for since the median and the altitude are the same since that's an altitude it's also median and it cuts this side and half so half 24 is 12 on each side she is going to be our 20 so we have to do a little side thing dear Hindu x squared + 12 squared equals 20 squared  turn so x squared + 140 equals 400 subtract the 144 from both sides go to x squared equals 256 Aurora take the square root 256 is a perfect square and it's 16 x 16 is 256 so it's 16th so now I know my height is 16 I can put that right there then just multiply 1/2 times 24 times 16 and your area will be 192 in squared  okay alright now  the cool thing about right triangles is Addison called Pythagorean triples right here it's a set of three positive integers a b and c satisfy a squared plus b squared equals c squared so it's whole numbers that work in the Pythagorean theorem K 3 4 and 5 is the most when is a green triple three four and five always make a right triangle no matter what 5 12 and 13 will turn 17 wheel in 7 24 and 25 will okay and bye bye - 2 * 364 * 2 is 85 * 2 is 10 6 8 and 10 would make a perfect right triangle and multiply them that one was by 2 If I multiply them all by 3 I will get 9 12 15 and so on and so on so ratio of 3 4 5 make a right triangle same thing with 5 12 and 13 5 * 2 is 10 12 * 2 is 24 and 13 times 2 is 26 that's just these x 2 they would make a perfect right triangle I can multiply mall by 315 120  I take that back  let's look at the wrong thing 15 how about 36 and 39 so any ratio 5 x 12 x  13 that will make a perfect right triangle anything that will reduce to 5-12-13 just we just talked about ratios in the last chapter same thing here I multiply mall by 2:16 3034 if you want find out Thru by 3 you get the point anything that is a ratio of 18 1517 and the same thing here turn off my mall by 2:14 4850 or the ratio of 7 x 24 x 25 x okay so look at example number 3 the cool thing about this is 345 is the biggest 1/5 1213 if you can memorize some of these Pythagorean triple turn even have to work out the problem you can just realize it's in that pattern in no the other side so scene example 3 find the length of the missing side using both with a green it's time triples so if I 14 and 48 that is Pythagorean triple because 14 + 4 8 fuel notice right here  okay 1448 n 50 meg Apothic right triangle how to realize that is 7 24 25 just x 2 I'm done now 345 is going to be turn you're going to recognize the medicine then 5 12 13 but it makes it a whole lot easier instead of having to do 14 squared using Pythagorean theorem + 40 squared + 50 squared well actually we would know that yet and this would be RX didn't know that site so 14 squared + 48 squared does equal 50 squared and it works in the Pythagorean theorem can you work that out okay guys last thing for this misses mostly 7.2 is remember that when we did the hinge theorem and the triangle inequality a triangle could only be formed when the sum of the smaller two sides were bigger than the largest side so when the Sun two smaller sides is greater in the third side we took the two short sides added it up and it had to be more than the third side or didn't make a triangle at all  there's also you can take that I can give you any three numbers in the first thing you're going to see it does it make a triangle and if it does you can tell if it's acute obtuse or right by using the if it works in the Pythagorean theorem then it has to be a right triangle and that's what's 7.2 that if C where is equal to a squared plus b squared then the triangle is a  right triangle who play know how can we tell if it's acute or obtuse well 7.3 tells us how to do that and we put it into the Pythagorean theorem but we know not going to be equal so what we do is if c squared is less than a squared plus b squared that means that what side is smaller then that means that angle has to be less than 90 which makes it a cute so if c squared is less than a square + b square then the triangle is acute  likewise if c squared is greater than a squared P Squared  then the triangle is obtuse so that kind of combines the Pythagorean what are my king stand that as you make the angle bigger that third side gets bigger okay so if we plug it into the Pythagorean theorem if it's equal  it's right if it's less than it's a cute and if it's greater than its obtuse so let's look at samples so number one first you want to see if it makes a triangle so here are biggest side  is 12 5 + 4 is 9 is 9 greater than 12 know so the two small sides are larger than third so this does not even make a triangle so not a triangle so we don't have to go on there because that doesn't even make a try look at this one biggest side 8 so that will be RC 6 + 7 that is 13 so that's bigger than night it makes a triangle so put it into the Pythagorean theorem here is to do the c squared first because if it's less than it's a cute if it's greater ketchup taste so I'm going to do c-squared and I'm not going to put equal to yet a squared plus b squared okay 8 squared  a squared 6 squared B squared 7 squared 8 squared - 64 6 + 49 that is 85 6464 is less than 80 that makes this an acute triangle okay alright let's do this one  alright turbo is the square root of 10 the biggest it is 3.16 so yes it is the biggest site so one plus is 4 that's greater than that so it makes a triangle so we want to do this and use the square root of 10 do not use that decimal and makes this much easier Seas a squared plus b squared I remember a square and a square root cancel each other out and you just get what's underneath so it's just 10 cancel that's one plus 91010 they're equal so what kind of triangle is that make it that makes it a right triangle so these make a right triangle 113 square root of 10 will make a perfect right triangle look at d of course the √ 27 Scooby the biggest know the square root of 9 is 3 √ 16 is 4 √ 27 is .2 - 3 + 4 is 7 so that's bigger than 5.2 so yes it makes a triangle now we need to square which side this is going to be my see okay so I'ma put that first the square root of 27 squared a squared would be the square root of 9 squared plus the square root of 16 squared when you square a square root you get the number underneath so those cancel I get 27  does cancel I get nine  first I get 16 what is 16 + 925  2727 is greater than 25 no remember it's greater its obtuse so that is an obtuse triangle okay guys alright so that's all for the 7.1 7.2 your assignment for that page is Page 436 number 3 through 27 multiples of 3 and number 34  also 1.2 is Page 444 number 3 through 24 multiples of 3 and then 30  35 and 37 okay then you also need to do 7.3 which will be another video

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7.1 & 7.2 Notes

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