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

3. Law of Cosines

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

Law of cosines is important because it helps us find the angles of a triangle, when doing SSS, or the value of two other sides in a triangle, when we have SAS, in this triangle 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 the 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 coordinate for angle B is acosC and asinC. Once we foil them our result should be: 

(http://math.ucsd.edu/~wgarner/math4c/derivations/trigidentities/lawofcosines_files/eq0002M.gif)

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 area of finding a triangle 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 use: 1/2bcsinA, 1/2absinC, and 1/2acsinB. 

References:

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

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

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

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