The Law of Sines
First of all this law is used whenever we get a non-right triangle in which the normal Trigonometric functions can't be used. This is used to find angles and sides of triangles with different angles and sides. The triangle should be labeled A, B, and C for the angles. Then after that we should label the sides with the same lower case letters, labeling the side opposite to the angle. You must divide the triangle into two creating a line representing the height and with that we can start to work with sines. From this point we can get two different equations. SinA=h/b and SinC=h/c. if we get these two formulas and divide them with each other we notice that we end up with the law of sines being SinA/a=SinC/c.
Area formulas - How is the “area of an oblique” triangle derived?
The formula of an oblique triangle that everyone know is Area=(h*b)/2. What we do here is that we want to use this same formula but to find a missing angle on the triangle that we don't know. Since we dont care about finding h what we have to do is substitute it. Through the knowledge that we have have of trig functions we know that we can replace h with something else. In this case h would equal a times the Sin A. this would be plugged in inside our old formula and eventually we would reach the point where our new formula would equal a = 1/2b(csinA)
This video went through how the formula is used and gives a more clear example oh how the formula comes from and how it should be used for these kinds of triangles.
Law of sines picture