The only problem I lost points on was the derivation of the law of cosines. I got the equations x^2+h^2=c^2 and (a-x)^2+h^2=b^2, but I couldn't connect them.
Here is how to connect the two equations:
First, factor out the (a-x)^2 to make the equation a^2-2ax+x^2+h^2=b^2
Then, replace the x^2+h^2 with c^2 using substitution to make the equation a^2-2ax+c^2=b^2.
Using the picture, it is possible to determine that cosB=x/c, or x=c(cosB).
Therefore, we can substitute this for x, making the final equation a^2+c^2-2ac(cosB)=b^2, or the law of cosines.
I am good at geometry so I liked this unit. I only had to memorize the formulas and apply them, which is what I am good at in math.
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