00:01
To solve a triangle in which angle a is 111 degrees, side a is 33 units, and side b is 11 units.
00:10
I'm going to arbitrarily choose this to be angle a at 111 degrees.
00:15
Across from angle a would be side a of 33 units.
00:19
And i'm just going to randomly choose this to be angle b.
00:22
I don't know its measurement, but i know that across from angle b is side b of 11 units.
00:27
That leaves this last one over here to be angle c.
00:32
Now the situation we have here is side side angle.
00:36
When we have side side angle, that is two sides and not the angle that is included, but on the outside of those two, we can use the law of signs.
00:46
The law of sign states that side a over sign of angle a is equal to side b over sign of angle b, which is equal to side c over sign of angle c.
00:58
So in our case, we have information about angle a, side a, so it definitely makes sense to use this part of the ratio.
01:06
And we also have information about side b.
01:09
So we can kind of ignore c over sign c for the time being.
01:14
When we fill in the given information, we have 33 over sign of 111 degrees equals 11 over sign of b.
01:21
If we want to solve for b, we must first focus on getting sign of b by itself.
01:26
So here we'll cross multiply.
01:29
After cross multiplying, we will divide both sides by 33 to get sign of b isolated.
01:35
At this point, we want to keep in mind the value of this piece of our equation here.
01:41
If this was a number that is bigger than 1 or smaller than negative 1, we would have an issue in calculating this.
01:50
But if you were to throw that into a calculator, you will quickly find out that it is not.
01:53
So we are good to keep going.
01:55
The same issue would arise in our next step anyway, but that is the reason for.
01:59
It.
02:01
So in order to get rid of sign and just leave us with angle b, we need to undo sign.
02:06
So we would use inverse operations here.
02:08
So inverse sign.
02:11
Inverse sign undes sign and just leaves us with b.
02:14
And if we throw this whole thing in the calculator, inverse sign of 11 sign of 11 .11 degrees divided by 33...