00:04
All right, this question gives us the diagram here of a 45 -4590 triangle, and we have provided information that the hypotenuse, the side c, is of length 6th.
00:15
Remember that from the 45 -4590 theorem, the hypotenuse, which is c, will always be the square root of two times one of the legs, and the legs will be the same length.
00:26
So we know here that a and b are going to be the same number.
00:30
The question is, how do we determine what that is? now, if we note here, so i'm going to just substitute the hypotenuse we know is c, right? that's the side of the triangle that is across from the 90 degree angle.
00:41
So we know that c is going to be the square root of two times a leg.
00:45
Well, the leg could either be a or b.
00:47
So let's just put a here.
00:49
And then just to make that a little bit nicer to look at, i'm going to switch the multiplication there, right, that is a square roots of two.
00:58
So what we know is that c is the same.
01:01
The hypotenuse is the same as a times the square root.
01:03
Square root of 2.
01:04
Now notice we were given c, right? we were told that c is a value of 6.
01:08
So we can actually substitute that in here, and we'll have 6 is a times the square root of 2.
01:15
Now what we need to do then is just find the value for a...