00:01
Upon the information provided, this would be a sketch of the diagram here with triangle abc.
00:05
The first thing we're going to do is find angle c since we have the pair of opposites there.
00:11
So i'm going to do law of signs for this.
00:12
So i set it up as sign of 37 over its opposite, which is 28, is equal to sign of the angle c, which i don't know, over 40.
00:21
So now i'm going to multiply out that 40.
00:23
So i have 40 times sign of 37.
00:25
And i'm going to divide that by 28, and that's going to equal to sign of c.
00:30
So next step here is first, make sure you're in degree mode on your calculator, but you're going to multiply 40 times sine of 37 and then divide that through by 28.
00:39
And i'm going to get a decimal here, which is 0 .897 is equal to sign of c.
00:46
So i'm going to take my sign inverse of that decimal and i get my first angle here.
00:51
So the measure of angle c is going to be about 59 point and if i round that to the nearest 10 to be about 50 .9 .3 degrees.
00:58
So the next step here is actually to figure out do we have a second triangle.
01:03
So sign is positive quadrants one and two.
01:06
We found the answer for quadrant one, which is for our first option for our second our triangle.
01:11
For our second triangle, we need to find the answer that the quadrants two.
01:14
So they have to have that same reference angle.
01:17
So i'm going to subtract 180 minus the 59 .3.
01:20
And i get 120 .7.
01:23
So the measure of angles c for my second option here is about 120 .7.
01:28
The one thing you do want to check is to make sure that if you added it to the 37 degrees i was already given, i do have room.
01:34
So in this case here, i do because if i added, i get 157 .7, which means if i were to subtract that from 180, i could find the measure of angle b.
01:44
In this case for that second triangle, which is 22 .3 degrees.
01:49
In the triangle on the right, if i do, or the first one, the c one, if i subtract 180 minus 37 minus the 59 .3...