 Hey and welcome to our first video in our series on trigonometry for electricians now trigonometry is a very important concept When we're dealing with electrical theory so much is based off of the right triangle Which we'll get into in other videos, but it's important for us to have the foundations of trig Now the beginnings of it are we're going to start with is Pythagoras's theorem Which if you remember from geometry in high school is just a squared plus b squared is equal to c squared Now the c squared is your hypotenuse side, which is going to be your longest side And generally what we're trying to do is figure out what the size of a side is not the square of the size of a side So what I want to do is I want to get rid of this square in order to do that I have to square root the c squared and to get the square out once I do something to one side of the formula I gots to do it to the other side So it ends up being c is equal to the square root of a squared plus b squared Let's see how that looks in a formula See what I mean here. I've got c is equal to the square root of a squared plus b squared Now let's throw this at a triangle and see practically how this will play out Trying to determine the sizes of the sides whether they be a and b or the hypotenuse c Now here, I've got us a right triangle We know it's a right triangle because I've got the square box here that tells me that that's 90 degrees Which also tells me that these other two angles have to add up to 90 degrees Because we know that all three angles in a triangle have to equal 180 degrees We also have a side and b side here, which will be given proper names in our next video But right now we'll just call them a and b and the important side here is this c side That is our longest side a k a the hypotenuse the hypotenuse will always be the longest side of a right triangle So if you calculate something and it works out to be smaller than a or b you've done something wrong And we also know that because it is opposite the 90 degree angle. So it will always be the longest side So let's throw some values at this a and b have given the values of four and five We're trying to determine what c is here now using Pythagoras's theorem We know that a squared plus b squared is equal to c squared So we know that the formula is going to be four squared plus five squared is equal to c squared So now that we've determined that c squared is equal to four squared plus five squared Let's get rid of these four squareds and five squareds. We know that four squared, which is four times four is equal to 16 Plus five times five, which is equal to 25 c squared is equal to 16 plus 25 Now that I've determined that c squared is equal to 16 plus 25 Why don't we just add 16 and 25 together and be done with it? So c squared is equal to 41 Now that I've determined that c squared is equal to 41. I'm not looking for c squared I'm looking for c so we need to get rid of this square somehow and like I said before We have to square root this side to get rid of the square Whatever we do to this side we have to do to this side. So c is equal to the square root of 41 So go ahead and punch that in your calculator C is equal to the square root of 41 and you're gonna work out that c is equal to 6.4 So congratulations, you've just solved for the hypotenuse, which is this c and so let's get rid of c and throw the answer in there So there we go now. We've determined that 4 squared plus 5 squared is equal to 6.4 squared Now what do we do though if we have a hypotenuse side in one of these sides and need to determine this side As we did before let's throw some numbers at it. I've got the hypotenuse is 450 and The B side or the A side is 225 Sorry the A side and now we want to determine what the B is so what we're going to do is let's plug into the formula We know that the formula is A squared plus B squared equals C squared or C squared is equal to A squared plus B squared So let's throw that in there. We know that 450 squared is equal to 225 squared plus B squared. Let's throw that into our formula Okay, so that we got that 225 squared plus B squared is equal to 450 squared Now we need to get B alone. So what we have to do is we have to subtract this 225 squared out of there Now even before we do that, let's get rid of these squares Let's figure out what 225 squared is and what 450 squared is and deal with those numbers first So we see that 225 squared actually works out to be 50,000 625 that's a big number plus B squared is equal to 202,500 Now we need to get B alone because we need to figure out what the B is right? We're trying to figure that out We can get rid of this 50,000 625 by subtracting it out of this side see this plus here that means that we have to subtract this to get rid of it as With any equation whatever you do to one side of the equation you have to do the other so B squared is going to equal 202,500 minus 50,000 625 So all we've done is we've moved the equation around here So we have B squared is equal to 200 and 2,500 minus 50,000 625 which works out to be 151,875 so we're getting closer to our answer B squared is equal to 151,875 as Before we need to get rid of the square that doesn't do us any good Let's square root the B squared and then let's square root 151,875 and get our answer because it's going to be B is equal to the square root of 151,875 So we're starting to see the answer get closer and closer here B is equal to the square root of a hundred and fifty one thousand 875 punch that into your calculator, and we get our answer of 389.7 So we have determined that 450 squared Minus 225 squared gives us three eighty nine point seven squared That is determined the size of B and that basically completes our walkthrough Pythagoras's theorem Doesn't matter if you have this side and this side you can go a squared plus B squared is equal to C squared Or if you have this side you're just going C squared minus This side is equal to this squared or C squared minus this squared is equal to this squared It's not too shabby at all. It's not too hard to walk through. This should just be a review from grade 12 Or not even grade 12 probably grade 10 geometry in our next video We're gonna start getting into some more trig functions Talking about the ratios of sides and starting getting it to sine cosine and tangent