BQ#1: Unit P: Concept 3: Law of Cosines SSS or SAS and Concept 4: Area of an oblique triangle

iii. 3. Law of Cosines - We need it because it allows us to find the missing sides and angles of oblique triangles with side angle side (SAS) or side side side (SSS). It is derived by making two right triangles, using the trigonometric ratios, and the distance formula. It is helpful and simple to understand. We derive it from a triangle in the first quadrant because all the ratios are positive and the origin is (0,0) making it all easy to derive. It works for a triangle with any lengths and with any angles. It will always work as long as the angles are realistic. The pictures below will walk you through it step by step. 

 
iv. 4. Area formulas -It is derived by drawing a line down the middle of the triangle and that creates two right triangles. Then you apply the trigonometric ratio and substitute that in for h. Now we have the area formula for an oblique triangle that looks almost the same to the one we know and love (A=.5bh), but we have our replacement for h, what h equals, and get the new formula (A=.5b(asinC)). The pictures below will walk you through it step by step.