1. Law of Cosines
We use law of Cosines to find the length of a missing side or degree of a missing angle in an Oblique triangle(No Right Angle)
In order to do this we must have some information and there are 4 conditions that will work, however only 2 use the law of Cosines, so we will focus on those today. A B C a b c
In order to use law of Cosines you must know:
1.) all 3 sides
2.) 2 sides and the included angle
The three angles are A, B, and C with the side opposite the angles being a, b, and c.
Using Logic for rule 1: as long as we know all three sides a, b, and c.
Using Logic for rule 2: If we know sides a and b and angle C.
If we know sides a and c and angle B.
If we know sides b and c and angle A.

2. a2 = b2 + c2 – 2bcCosA b2 = a2 + c2 – 2acCosB c2 = b2 + a2 – 2baCosC
Law of Cosines
Law of Cosines: when you know 3 sides.
Law of Cosines: When you know 2 sides and the included angle.
a2 = b2 + c2 – 2bcCosA
b2 = a2 + c2 – 2acCosB
c2 = b2 + a2 – 2baCosC
These are the same equations they have just been solved for different parts.

3. B 11 8 C A 5 Cos A = (112 + 52 – 82)/(2(11)(5)) Cos A = A = cos-1 (
Cos B = ( – 52)/(2(11)(8))
Cos B =
B = cos-1 (
B = A 5
C = A – B
C =

4. C
#15 9 6 A B 4

5. C 2 45º A B 4 b2 = 42 + 22 -2(4)(2)cos 45º b = √ b =
Cos A = ( – 22)/(2(4)()
A = cos-1 (
A =
C = 180 – 45 –
C =

6. #10 C 3
30º A B 4

7. Assignment #9 Pg. 535 (9-16)