BQ#1: Unit P Concept 4 : Area of an Oblique Traingle.

1. Law of Sines - Why do we need it? How is derived from what we already know?
The law of Sines is used for non-right triangles. For example, trig function is used for right triangles only.  We need the law sine in  order to find a side while we know the opposite angle. Triangles like AAS OR ASA, need to determine all three angles and sides.
It is derived by drawing a perpendicular line across from angle B. This will be called height. Once we have a height, we can solve any angle by using SOH CAH TOA. You equal the equation of the angle with the equation of the opposite side, and solve.

4. Area Formulas - How is the "area of an oblique" triangles derived? How does it relate to the area formula that you are familiar with.
The area of an oblique triangle is derived by having two side and one angle. The height is unknown, so we use the formula 1/2b(csinA). This equation is one out of the three that can be used, since we have three sides and angles. It all depends what they give you to start with. All students are familiar with A= 1/2bh to find the area of a triangle. This formula was used since they would give us the height. Now we do not get the height, so we substitute it with a side(sine of and angle).