1. 2) State the LAW OF COSINES.
Students,
Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary.
1) State the LAW OF SINES.
2) State the LAW OF COSINES.
3) Solve for c.

2. Definition: Law of Cosines
The last two cases (SSS and SAS) can be solved using the Law of Cosines.
(The first two cases can be solved using the Law of Sines.)
Law of Cosines
Standard Form
Alternative Form
Definition: Law of Cosines

3. Application: Law of Cosines
Two ships leave a port at 9 A.M. One travels at a bearing of N 53 W at 12 mph, and the other travels at a bearing of S 67 W at 16 mph. How far apart will the ships be at noon? N
At noon, the ships have traveled for 3 hours.
53
43 mi
36 mi
Angle C = 180 – 53 – 67 = 60 c
60 C
48 mi
67
The ships will be approximately 43 miles apart.
Application: Law of Cosines

4. Definition: Heron’s Area Formula
Given any triangle with sides of lengths a, b, and c, the area of the triangle is given by 5 10 8
Example:
Find the area of the triangle.
Definition: Heron’s Area Formula

5. 1) Find the area of the triangle with side lengths of 8 meters, 7 meters, and 14 meters.

9. Complete each identity.