00:01
We're given the trapezoid abcd, where we're told that the angle at a is 45 degrees, and then we have numerous 90 degree angles, and we know the length of one side.
00:17
So if this here is angle b, then we'll call this side b, we'll call this side d, we'll call this side a, and that is also c then.
00:32
And because we know that angle a is 45 degrees and angle b is 90 degrees, then this angle here must also be 45 degrees, because the angles of a triangle add up to 180, and it means that this one is also 45 degrees, because angle d is 90 degrees, and 45 plus 45 adds to 90, and then because this is 45 degrees, then this one is also 45 degrees.
01:07
So we know all our angles now, so we just have to calculate the sides.
01:14
Well, i can use the law of sines for that.
01:19
The law of sines says that a over sine alpha is equal to b over sine beta is equal to c over sine gamma, where alpha is the angle opposite of side a, beta is the angle opposite of side b, and gamma is this angle opposite of side c.
01:49
So if i look at a, or i call alpha is angle a, beta is angle b, then, which is here, i'm looking at the 90 degree one, so instead of b, i'm looking at the 90 degree one...