BQ #1- Unit P: Concepts 1&4: Law of Sines AAS or ASA and Area of an Oblique Triangle

i-Law of Sines:
Why do we need it?
The law of sines is of importance because it helps us to find non-right triangles that are commonly seen in the real world. With this we are able to find any unknown angle or side if we have already found or were given two angles and one side as well we could have been given two sides and one angle.
How is it derived from what we already know?

http://i1.ytimg.com/vi/Bj7h6OMBvqk/hqdefault.jpg

 When given an unknown triangle with some given information on the side and two angles, when deriving it we can just form a line straight down from the middle to give us two 90 degree triangles. With this we can use Sine and it will  be something as below where we get a ratio. However since we want Sine by itself we multiply through to receive the final answer.

http://www.lhs.loganschools.org/~rweeks/trig/law_of_sines.jpg

iv-Area Formulas:
How is the "area of an oblique" triangle derived?
 When given a triangle with some of the given angles and side we just cut the triangle in half for we can receive two 90 degree triangles. With this we then use SOHCAHTOA to get a ratio, with this we can substitute it in for the height of the area formula we are used to, for we can use to solve the area of the triangle.

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRUfaYjkTy5hlsAuerPsDTfulo_zx2qECBMGIWGwX-EcYy4zuaMlV3LC1XqmMsvMpN1kXNTXUSw9HJScLKdDdZdydgqvLghasCFxtONLYiSbtPDbOBMUe9xWWI1TqvDtxuW0-MR7RxxZY/s400/hi.bmp

How does it relate to the area formula that you are familiar with?
This relates to the area formula (a=1/2bh) that we are familiar with because we solve with this formula however we substitute "h" with 1/2abSinC or any of the others.

References:
http://www.lhs.loganschools.org/~rweeks/trig/law_of_sines.jpg
http://facstaff.gpc.edu/~ahendric/Math1113/sec6_1notes/images/pic010.jpg
http://i1.ytimg.com/vi/Bj7h6OMBvqk/hqdefault.jpg
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRUfaYjkTy5hlsAuerPsDTfulo_zx2qECBMGIWGwX-EcYy4zuaMlV3LC1XqmMsvMpN1kXNTXUSw9HJScLKdDdZdydgqvLghasCFxtONLYiSbtPDbOBMUe9xWWI1TqvDtxuW0-MR7RxxZY/s400/hi.bmp