Videos

Solving Right Triangles Notes

Added Feb 03, 2015 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//hs.cantonisd.net/apps/embed/?v=71903" frameborder="0" allowfullscreen></iframe> Change dimensions

Show Transcript

okay we're going to wrap it chapter 7 on right triangles now we're going to bring everything together that we have learned to solve a right triangle and when it says to solve a right triangle it means to find all of its sides and all angles so you know every single part of the triangle now we've learned several different methods for that now the first one of course that we learned was the factory in theorem can remember the Pythagorean theorem is a squared plus b squared equals c squared snap we use the Pythagorean theorem when we already know two sides and we need to find a third side pay the next was the geometric means and remember the geometric means is used when the big triangle is a 90° angle and you draw altitude that starts at the right angle and goes to the hypotenuse so this splits the hypotenuse into two different part so you have Segment 1 and segment 2 out of the whole hypotenuse and then remember the segment or the leg by segment one is the short leg the leg by segment 2 is the long in this is the altitude they'll remember that the altitude is the geometric means between the two some altitude is geometric means between Segment 1 and segment 2 so altitude goes in the geometric means cross in Segment 1 and 2 in extremes cross now remember the other geometric means was that the leg and it didn't matter if it was short leg or long leg the leg is the geometric of the segment that is adjacent the one touching so short leg is one long leg would be too and the entire hypotenuse so Legos in cross for the means and the segment adjacent  in the hypotenuse ear what they are the geometric mean for in those go in the extreme cross so to use geometric means but they rent there and we need two sides to make geometric means we need any two-part so we could be segment one in the hypotenuse it could be the long leg and segment 2 it just needs to have any two parts to it okay the next one is two special right triangles now the special right triangles where the 45-45-90 which meant that the short equal they're the same in the hypotenuse was the leg times the square root of 2 are other one was a 30-60-90 and remember the side across from the party is the short leg it is X and that's what everything is based on the hypotenuse is 2 times the short leg and the long leg across from the 60 is the short leg x times the square root of 3  now to use one of the special right triangles you have to have either of 45 45 90 or 30 60 90 and you only need one side for that but it can only be one of those too okay the next way is trig so remember that trig you can use sohcahtoa to remember sine cosine and but if you will remember that sign is opposite over hypotenuse cosine is adjacent over hypotenuse and tan is opposite over adjacent now when we use trig we need to know at least one angle and one side so you'll notice that what is needed is different for each one now remember that trig is to find sides not angles okay okay the last way is envy trig now remember inverse trig is to find angles not sides into you inverse trig you need to know at least two sides and you can find the angles that are missing so we have inverse Universe cosine and inverse tangent and those are still offered over hypotenuse adjacent over hypotenuse and opposite over adjacent okay now let's apply that in solve a couple of right triangles okay we are given that this bottom side is 10 and this one angle is 40 so you need see you have one angle one side look back at the front page you'll see that you're going to use trig now we need to solve for this when will they may we need to stop for the hypotenuse is B and then we also need to find this angle up here now if we know this is 40 that's 90 we just subtract from 9040 and we will get that top angle which will be 50 degrees so there's our first answer now let's find first so if we have 40 and we have this side 10 that would be the opposite of 40 and this would be the adjacent for you because be is our hypotenuse no opposite over adjacent is tangent so if we do the tan of 40 degrees equals office stay over adjacent 10 remember we put this over one cross multiply a equals 8.4 so that side now let's fine be now be you have many option cuz you already know Sade and  you already know this is 10 so we need the hotness is one of them so it's definitely got to be sign or cosine but you can pick which one if we use the adjacent this 10 that we already know we can use the cosine that would be cosine of 40 degrees equals the adjacent 10 over the hypotenuse B now remember Lil trick if the variable is on the bottom we switch these two so the B goes here the cosine 40 goes here so now we just do turn the volume by the cosine of 40 and you get 13.05 so now we have every part of this triangle every side and every angle and that's how you solve a right triangle so let's look at number 12 okay looking at number 12 or given to we're giving this leg is 6 in the hypotenuse is 10 if we have two sides we can use the Pythagorean theorem now if you look really close you'll notice that this is actually Pythagorean this side is 3 * 2 in the side is 5 * 2 so this shot side should be four times too which is 8 so if you notice that you can this side with an 8 automatically and you're done but if you didn't notice that you're going to use the Pythagorean theorem on here and that side of C and you would just do 6 squared plus b squared equals 10 squared + that's 36 plus b squared equals 100 subtractor 36 on this side and B squared equals 64 take the square root of both sides and B equals 8 so you get the same answer okay now what we need to do is find the angle so let's label them A and B so if we need to find angle a first okay look at what side you're given okay you can use any three of these so you can use sign cosine or tangent it doesn't matter let's say I'm one of use tangent so the tan of angle a is the opposite 8 play Jason 6 so remember I want to soft rain and get by itself so I need to move tangent to this site so a equals and when you move over it becomes the inverse of that 8/6 type that in your calculator exactly like it looks and you were going to get 53 1 degrees so that's angle a to find B you can just subtract from 90 or you can do another inverse trig function we just do 90 - 53.1 we are going to get 36.9 so be has to be 36.9 and if you I'll get all then it works out just perfectly so if you label that and let's say let's just go ahead and round to the nearest degree this one's going to be 37 and this one is going to be 53 which adds up to 90 so we saw for every angle and every side okay in the last problem number 13 don't look they only give us one side your automatic response was probably to use trig because we have one angle in one side but if you will stop and think about this is a 30 degree angle so what does that make this one well subtract from 90 you get 60 so actually you have a special right triangle 369 and you have been given the hypotenuse will if you'll remember right the short leg across from the 30 right here the short leg it's half of the hypotenuse so half a 24 is 12 and then the long leg is the short leg times the square root 3 so that's 12 the square root great and you were actually done with that problem that's all you have to do now you could have used trig to solve it and of course it would take a whole lot of steps but if you'll think about those special right what was it in use them when you see him it's a lot faster for this you have a worksheet and you will get it in class on Tuesday if you have already gotten it

Uploaded by Pam Chastain.

Videos

Solving Right Triangles Notes

More videos from Pam Chastain