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

( (http://math.ucsd.edu/~wgarner/math4c/derivations/trigidentities/lawofcosines.htm)   

3. Law of Cosines

Law of cosines is important because it helps us find the angles of a triangle, when using SSS, or the value of the other two sides in a triangle, when we have an SAS triangle. In this picture angle C is the vertex, angle B is acosC and asinC, and angle A is at (b,0). 

( (http://www.themathpage.com/atrig/Trig_IMG/cos6.gif)    

To find our coordinates we must first draw a line going down our triangle and we end up with two right triangles. For this problem we will be using c^2=a^2+b^2-2abcosC. Since our angle B is now made up of two angles we solve for side b, which is made up of x and b-x. The coordinates for angle B is acosC and asinC and we foil them. Once we foil them our result should be: 

(http://math.ucsd.edu/~wgarner/math4c/derivations/trigidentities/lawofcosines.htm)

4. Area Formulas

(http://www.compuhigh.com/demo/lesson07_files/oblique.gif)

For the area of an oblique triangle we have to use the formula of finding the area of a triangle, the formula is 1/2bh. As seen in the picture above we draw a line going down the triangle so we have the height of the triangle. Also, depending on what angle we are solving for we can have three different formulas to solve with. The formulas are 1/2bcsinA, 1/2acsinB, and 1/2absinC.

References: 

http://www.compuhigh.com/demo/lesson07_files/oblique.gif

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

http://www.themathpage.com/atrig/Trig_IMG/cos6.gif