00:01
Okay, so this question provides us with these measures and asks us to determine the number of possible triangles, find the measures of the three angles of each possible triangle.
00:11
So what we're going to start with here is we've got an acute angle, and we're going to use the law of signs to find the other angle.
00:20
And so what we've got is a over the sign of a is equal to b over the sign of b.
00:28
And i've drawn out a little guesstimate of what this triangle can look like.
00:35
And so here we've got 8 over sine of a, sign of 45 degrees, is equal to b, which is 10, over sign b.
00:47
And then when you cross multiply and divide by 8, i get that sine b is equal to 10 times the sign of 45, which is the square root of 2 over 2, divided by 8.
01:01
And so then when you use your calculator to find out what this is, it's 0 .883 is sign b.
01:12
So when we use the rules that are provided in this chapter on page 571, we get that our angle is an acute angle.
01:22
And so now because we have b less than one, we want to find the two possible values of this b here.
01:31
And so when we take the inverse sign of this, we get that the measurement of angle b is 62 degrees.
01:40
And then we also have a measurement of a b prime that's one minus this 62...