1. LAW of SINES
Standard Cases

2. Exploring area further
No matter which pair of sides and included angle we are given, the area of a triangle does not change. Hence,
Multiplying by 2
x 2
x 2
x 2
Dividing by (abc)
Exploring area further

3. Exploring area further
This gives us the result that, in a given triangle, THE RATIO of the Sine of an angle to the length of its opposite side is equal for all three pairs of opposites in the triangle.
THE LAW OF SINES
This result is
Exploring area further

4. There are two basic cases for using the law of sines
There are two basic cases for using the law of sines. Both are 2 Angle Cases.
AAS - If you are given two angles and a side NOT between them.
ASA – If you are given two angles and the side between them.
Note: When using inverse sine to find angles, pay particular attention to the indicated SIZE of the angle. The inverse sine will only give you answers between 0 and 90 degrees for a triangle. However, angles CAN be obtuse, so you must make the proper adjustment. This is the case (possibly) in #11 of the homework.
The Law of Sines

5. Solving Using Law of Sines
Write down a list of all 6 parts of the triangle.
Fill in what you know.
Find the EASIEST missing piece first.
Use proportions (from the Law of Sines) to solve for the missing pieces.
Solving Using Law of Sines

6. In Triangle ABC, B=64o, C=38o, and b=9 ft
In Triangle ABC, B=64o, C=38o, and b=9 ft. Find the unknown measures of the triangle.
Example 1

7. In Triangle ABC, a=10 m, b=3, and A=100o
In Triangle ABC, a=10 m, b=3, and A=100o. Find the unknown measures of the triangle.
Example 2