1. Law of Sines
We use law of Sines to find the length of a missing side or the degree of a missing angle in an Oblique triangle(No Right Angle) A B C a b c
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 Sines, so we will focus on those today.
In order to use law of Sines you must know:
1.) 2 angles and 1 side or
2.) 2 sides and an angle not between them(not included)
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 two of the three angles A , B, or C and one side a , b, or c we can find both the other sides and the other angle.
Using Logic for rule 2: if we know sides a and b then we need to know an angle other then C. If we know sides a and c then we need to know an angle other then B. If we know sides b and c then we need to know an angle other then A.

2. Law of Sines
There is one last rule we need to recall from Geometry before we can start plugging away at these problems. The sum of the 3 angles of a triangle add to = ? Do you remember?
1800 or A B C a b c
The three angles are A, B, and C with the side opposite the angles being a, b, and c.

3. Lets look at some problems:C a b
C = 20
1050
400
Lets look at some problems:
Step 1 find the third angle using the sum of the angles of a triangle.
A = 180 – 105 – 40 = 350
Step 2 Since we know C and c and all the angles we will use c/Sin C = (pick which one you want to find first)

4. You Try A Lets look at some problems: #21) b c = 3 C B a
1100
Lets look at some problems: #21)
300
Find: B , b, a

5. What if you are given 2 sides and and an angle.
Ex. A = 600 a = 9 c = 10 A B C
a = 9 b
c = 10
600
Always draw a diagram first, and fill in the given information
In this situation we use the law of Sines reciprocal (flipped)
We always use the Angle and side we know both of.
Use the original form of law of Sines
B = 180 – 60 – =
b = 7.45, B = , C =

6. You Try
Use the law of Sines to solve the triangle round your answers to 3 decimal places.
#27.) B = 1000 , c = 3, b = 5
#30.) b = 2, c = 3, B = 400

7. Assignment # 22
Pg. 527 – 528
(9-23 odds)