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.

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

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

Example: Law of Cosines - SAS B 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

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

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

Complete each identity.