BQ #1: Unit P Concepts 1 & 4: Law of Sines and Area Formulas

1. Law of Sines: Why do we need it?  How is it derived from what we already know?
We use the law of sines to solve for non-right triangles.This formula helps us find missing sides or angles when we only have AAS (angle, angle, side), ASA (angle side angle), or SSA (side, side, angle). We use the trigonometric function of sine to derive the formula and form two right triangles then we are able to derive for the formula. But before we do, we will have to add other variables to make it possible, like 'h' for the height (perpendicular to the base). If we draw a perpendicular line, we will get our 2 right triangles, which we need to derive for the formula. The following pictures go over the derivation of the formula.

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 of an oblique triangle is derived from the area of a triangle formula: A=1/2 bh. This formula allows us to find the area of a triangle without having to know what the value of "h" is. The formula for an oblique triangle is similar to the formula of a regular triangle because they both have the same purpose and the same root or origin. The only difference is that in the original formula we must know the value of "h", but in the oblique triangle formula we don't need to know the value of "h" because instead we will be using one of the angle measures. The picture below will go over the derivation of the formula.