Use+the+Law+of+Cosines+to+Solve+Triangles

This page will teach you how to use the Law of Cosines to solve triangles. I enjoyed this section of Trig because it provides a formula that is useful in many other sections of the Trig Unit. The Law of Cosines can be applied to nearly any triangle and can be used to find almost every angle or side when given S-A-S or S-S-S. For the most part, this objective was easy for me except for when the Ambiguous Case appears. I had a hard time understanding when this case occurs and how to get around it. PORTFOLIO PROBLEM IS AT THE BOTTOM OF THE PAGE:) By: Katelyn McCann Period 7 __**VIDEO TUTORIAL**:__ http://www.youtube.com/watch?v=islS9GMGHfQ&feature=plcp&context=C4f08c5dVDvjVQa1PpcFP4YOHE38-3LlDSbioyRhhGebGEEzbdQhw%3D

__**Deriving the Law of Cosines:**__ 1.Start by writing out the pythagorean theorum for bothpieces of the triangle: h^2 + (a-x)^2 = c^2 h^2 + x^2 = b^2

2.Rearrange the first equation so that it solves for h^2 h^2 = c^2 - (a-x)^2

3.Plug in the equation in Step 2 for h^2 in the 2nd pythagorean equation from Step 1 c^2 - (a-x)^2 + x^2 = b^2

4. Multiply out (a-x)^2 c^2 - a^2 + 2ax - x^2 + x^2 = b^2

5. Cancel out the -x^2 and the x^2 b^2 = c^2 + a^2 + 2ax;

6. Get rid of variable x cosC = x/b; x = bcosC

7. Plug in bcosC for x
 * c^2 = b^2 + a^2 - 2abcosC**

__**Using the Law of Cosines**__ The Law of Cosines can be applied to any triangle that has SSA or SAS (Side Side Angle or Side Angle Side)


 * Easy example:**




 * Middle Example:**
 * Hard Example: Find X, Y, and Z**



__**PORTFOLIO PROBLEM:**__


 * Solve this triangle using Law of Cosines given a, b, and c.**
 * a = 15**
 * b = 20**
 * c = 25**