Video instructions and help with filling out and completing Which Form 2220 Determining

Instructions and Help about Which Form 2220 Determining

All right in this video we're going to do an example of finding an angle the measure of an angle if we know a little more information so in this case suppose we know the cosine of theta is equal to square root of 3 over 2 we want to find the angle what the measure is for angle here theta so remember cosine of an angle is defined to be the adjacent side over the hypotenuse and again for our angle theta this would be the adjacent so I'm simply going to label the adjacent side as square root of 3 I'm going to label the hypotenuse here with length 2 and now we would have to figure out you know this missing side you may know this you know if you from geometry but we can always figure it out just using Pythagorean theorem so we'll take the square root of 3 squared plus this missing side we'll call it B squared that equals 2 squared well the square root of 3 squared is just going to be 3 plus B squared 2 squared is going to give us 4 and now if we subtract 3 from both sides we'll just get that B squared equals 1 and when we take the square root we'll get positive negative 1 but again it's got to be the positive one because we're talking about a length here so this simply has a length of 1 so again what we're trying to do is we're trying to figure out our our angle theta so now we have to be a little bit clever here and what we're going to do is I'm going to kind of take this triangle and I'm going to reflect it okay so we've got our triangle here this has length 2 this has length 2 this has length 1 this has length a square root of 3 but I don't really care about that I'm going to imagine sort of a just reflecting this triangle over to the other side ok so just imagine it sort of getting reflected over it's going to go down here so we reflect it over it's going to come down here okay so this was length 2 okay so this is not great artistry here but if it's the same triangle this had lengths to this had linked 1 that means the hypotenuse here would have length 2 and this other side again would have length 1 but if you think about it now what we really have is we've got an equilateral triangle because this is length 2 this is length 2 this entire length adds up to 2 so that means since all the side lengths are the same that means all the angles inside are the same and since all the angles have to add up to 180 degrees we know that each one of those angles has to be 60 degrees individually so ok so that means again this angle is 60 degrees but notice our little angle theta here that was kind of sitting you know kind of sitting in this uh this upper region right this whole angle if we trace it out that's what's going to be 60 degrees so in this case theta is only going to be half of that so we would have to take our 60 degrees and divide it by two and that would simply give us that theta has the measure of 30 degrees or we could put that in radians and say that's PI over 6 radians