0:00
All right, welcome back.
00:01
So for this problem, we're given side b is equal to four, side c is equal to six, angle b is equal to 20 degrees.
00:13
All right, so we have this nice sighting angle pair right here.
00:17
We can use the lot of signs.
00:22
So sign of 20 degrees divided by four is equal to sign of angle c.
00:33
Which is just going to see divided by six right side c or we can multiply both sides by six that will give us i'm going to simplify a little bit right here right because this was a six and then a four just divide everything by two and then we can solve for this left hand side um find out what it is in decimal form put a point five one three i go to sign we'll take the inverse sign of both sides which means that c is equal to 30 .9 about degrees all right so does this give us two solutions well let's find out so this is one value for c right here if we do 180 minus 30 .9 degrees we get 100 and so 149 .1, 149 .1 degrees, which when we add that, 20 to that, it's still less than 180 degrees.
02:07
So this is also another solution for c, for the angle c.
02:12
So we've got two solutions here.
02:15
The first one, which i'll do in blue, the english is equal to 30 .9, which that would mean that angle a, equal to 180 degrees minus, oops, 180 minus 30 .9 minus 20 degrees, right, angle b.
02:37
So then a would be equal to, so that's 30 .9, not a 36, is equal to 129 .1 degrees.
02:51
Okay, if that is the case, then side a, let's see what is it? we find it by 8 over a sign of angle a, which should be equal to, oops, b, which is equal to four, divided by sign of 20 degrees...