00:01
So in this problem, we're being asked to solve the given triangle.
00:03
So let's go ahead and draw this triangle.
00:05
So we have triangle a, b, and c.
00:08
We know angle a is 45 degrees.
00:10
Side b, that's opposite angle, b is 7, and side c, which is opposite angle c, is 8.
00:15
Well, because we have two sides in the included angle, we can go ahead and solve for side a by using our lair cosine.
00:22
So the lair cosine says that a squared will equal to b squared plus c squared, minus 2 times b times c times the cosine of angle a.
00:32
So to solve for a, we would then just take the square root of both sides.
00:36
So let's substitute in our values.
00:38
So a will equal to the square root of 7 squared plus 8 squared minus 2 times 7 times 8 times the cosine of 45 degrees.
00:47
So now we can actually go ahead and type this into our calculator.
00:51
So we're going to have the square root of 7 squared plus 8 squared minus 2 times.
00:57
7 times 8 times the cosine of 45 degrees.
01:01
And it doesn't look like you were told what's around to, so i'll just round one place after the decimal...