BQ#1 - Unit P

BQ#1 - Unit P 

1. Law of Sines - Why do we need it?  How is it derived from what we already know?  

Here we have the non-right triangle and once we make a line straight down from B we get two right triangles and could use what we know with the trig functions.

To derive the Law of Sines we know that to get A we need to use Sine and get the opposite/hypotenuse giving us h/c. We multiply both sides by c to get h by itself. And now have cSinA=h. We must also do the same to get C. Taking the same steps as A, we will get aSinC=h. Since both equal h, this means they both equal each other, cSinA=aSinC. We now need to get SinA and SinC by themselves, so we divide both sides by ac. And c will cancel out on one side and a will cancel out on the other leaving us with SinA/a=SinC/c

1. 1. 
      
   
   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?
   
   We derive this formula because we first know the original equation is A=1/2bh. We dont know the h so to find this we must use the trig functions. We know that the SinC=h/a and to get h by itself we multiply each side by a. We now replace h with aSinC giving us A=1/2b(aSinC).
   
   
   This relates to the original area formula because we are using the exact same formula except replacing h because in order to find h we must use the trig function. And instead of just finding h and plugging it in, we plug in the trig function to find h in the original equation.