1. Law of sines: The main reason we need law of sines is to find unknown parts of a non right triangle. How ever in order to use law of sines we must be given either AAS, ASA or SSA.
As shown on the video we start with a triangle labeled ACB. We must drop a line from angle C in order to make 2 right triangles. From there we can figure out that the sin of a=h/b. Also that the sin of C=h/a. Then if you divide by ab you get sinA/a= sinC/c with is the law of sines.
4. This video will go over how the area of an oblique triangle is derived.
Our regular formula is area=1/2*bh. The new area formula is a=1/2*b(asinC) They relate because essentially they are the same formula the only difference is that we have solved and substituted for h. When we made the oblique triangle into a right triangle we used our knowledge of trig functions to find the h=asinC. This then goes into our normal formula giving us our new formula that now works for all triangles.