3. Law of Cosines - Why do we need it? How is it derived from what we already know? The derivation must be shown either in a video or in multiple sequential pictures and inshould include descriptions and information beyond what you can find in the SSS.
This video derives the law of cosin starting off by starting off with the use of the trig value functions such as sin= opp/hyp We start off by cutting or triangle and dividing line is labeled as h. Since SinC=h/a we multiply a on both side and get h=asinc. He then speaks of how the sides are achieved. Using the Pythagorean theorem A^2+B^2=C^2 we take the squared values of the legs of a triangle and set it equal to our hypotenuse. Leading into identities sinC and cosC are equal to one.
4. Area formulas - How is the “area of an oblique” triangle derived? How does it relate to the area formula that you are familiar with?
The area of an oblique triangle is taking from the original area equation of a triangle. We take the SinC=h/a we multiply each side by the value of a and get h=asinC. We then take our our original area of a triangle formula and replace the h with our h value in which results in a=1/2absinC. We can do this with our a and b values. For example if we use Sin A= h/c multiple each side by c and get h=csinA and plug it into our orignial equation of 1/2bh replacing the h. So our new equation would be sinA=1/2bcsinA.