1. 1) Solve the triangle. Students,
Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary.
1) Solve the triangle.

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. Example: Law of Cosines - SSS
Find the three angles of the triangle. C B A 8 6 12
117.3
26.4
36.3
Find the angle opposite the longest side first.
Law of Sines:
Example: Law of Cosines - SSS

4. Example: Law of Cosines - SASB A
6.2
75
9.5
Solve the triangle.
67.8
9.9
Law of Cosines:
37.2
Law of Sines:
Example: Law of Cosines - SAS

6. 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

7. 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

10. Complete each identity.