Transcript Chapter 5

Section 8 – The Law of Cosines
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)
Derivation
 C2 = (a-x)2 + h2
 C2 = a2 - 2ax+x2+h2
 C2 = a2 - 2ax+b2
 C2 = a2 - 2a(bcosC)+b2
 C2 = a2+b2 - 2abcosC)
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
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
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.
Assignment
 Chapter 5, Section 8
pgs 331-332
#12-24E,30