1. Section 8 – The Law of Cosines
Chapter 5
Section 8 – The Law of Cosines

2. The Law of Cosines
Just like the Law of Sines, the Law of Cosines incorporates the sides and angles of any triangle.
Law of Cosines
a2 = b2 + c2 – 2bc(cos A)
b2 = a2 + c2 – 2ac(cos B)
c2 = a2 + b2 – 2ab(cos C)

3. Derivation C2 = (a-x)2 + h2 C2 = a2 - 2ax+x2+h2 C2 = a2 - 2ax+b2
C2 = a2 - 2a(bcosC)+b2
C2 = a2+b2 - 2abcosC)

4. Examples Solve each triangle below.
EX 1: A = 120 degrees, b = 9, and c = 5
EX 2: B = 65 degrees, a = 8, and c = 3

5. Heron’s Formula
Heron’s Formula is a formula used to figure out the area of any given triangle when you have the perimeter of the triangle
where s is the semiperimeter

6. Example
EX 3: Use Heron’s Formula to figure out the area of a triangle with sides 6, 8, and 13.
EX 4: Use Heron’s Formula to figure out the area of a triangle with sides 5, 8, and 19.

7. Assignment
Chapter 5, Section 8
pgs #12-24E,30