1. Bridge Design A bridge is to be built across a small lake from a gazebo to a dock (see figure). The bearing from the gazebo to the dock is S 41 W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74 E and S 28 E, respectively. Find the distance from the gazebo to the dock.

3. Finding the Area – Using the Law of SinesB
* Draw an altitude from vertex B. c a A b C

4. Are there unique triangles with the side and angle measures given above? Why?
Why can’t the Law of Sines be used to determine the measures of the missing angles and/or sides?

5. Complete the Law of Cosines
Activity …

6. NOTES (Law of Cosines 16.2)
 LAW OF COSINES:
a2 =
b2 =
c2 =

7.  Use Law of Cosines to solve for Cos A.

8. Law of Cosines (solving for angles)
Cos A =
Cos B =
Cos C =

9. Solve for all missing information …

10. EXAMPLE 1: Two ships leave at 4pm
EXAMPLE 1: Two ships leave at 4pm. One is headed at a bearing of N 38 E and is traveling at 11.5 miles per hour. The other is traveling at 13 miles per hour at a bearing of S 47 E. How far apart are they when dinner is served at 6pm?

11. EXAMPLE 2: The distance on a map from the airport in Miami, FL, to the one in Nassau, Bahamas is 295 kilometers due East. Bangor, Maine is northeast of both cities; its airport is 2350 kilometers from Miami and 2323 kilometers from Nassau. What bearing would a plane need to take to fly from Nassau to Bangor?