Answer:
Explanation:
It looks like you are going to be using the sign law. Luckily, the givens are in the form of ASA where the side is between the two given angles.
The very first thing you should do is find W.
W + 81 + 30 = 180. Every triangle = 180 degrees. Combine the left.
W + 111 = 180 Subtract 111 from both sides.
W+111-111 = 180-111 Combine
W = 69
=======================
The second thing to do is to set up the sine law.
Equation
19/Sin(W) = x/Sin(30)
Givens
Sin(69) = 0.939958
Sin(30) = 0.5
Solution
19/0.939958 = x/0.5 Multiply both sides by 0.5
19*0.5 / 0.939958 = x
9.5 / 0.939958 = x
10.1758
Answer
x = 10.2
Notes
1. There are all kinds of ways to set up the sine law. It is a proportion. For example it can be set up as Sin(W)/19 = Sin(30)/x but this requires that you do an extra step, and in math you want to avoid any extra steps.
2. There are other ways of doing the question, but they all come back to the sine law. For example, you could find WV from the sine law. That would mean sin(69) / 19 = Sin(81)/WV but that involves 2 or 3 extra steps.
3. The way I have done it is the simplest and most straight forward way.