BQ# 1: Unit P

1. Law of Sines - 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 should include descriptions and information beyond what you can find in the SSS.

We need the law of sines to solve for triangles that are not 90* triangles. With the triangle having sides a, b and c, and angles A, B and C, C can be cut down to make 2 90* triangles. Using opposite over hypotenuse, the trig functions are rearranged. When everything is then equal to height, and everything is simplified, the law of sines is done.

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 is derived from the original a=(b)(h) but the change is that instead of all 3 sides given, only 2 sides are given, with 1 angle (SAS). There are 3 given formulas we can use, depending on what information is given to us, but it is just a matter of manipulating the formula to get what we need.

Either: Area = 1 ab sin C 2

Or: Area = 1 bc sin A 2

Or: Area = 1 ca sin B 2

REFRENCES:

http://math.ucsd.edu/~wgarner/math4c/derivations/trigidentities/lawofsines.htm

http://www.mathsisfun.com/algebra/trig-area-triangle-without-right-angle.html