Bridge Design A bridge is to be built

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.

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

• 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?

NOTES (Law of Cosines 16. 2) LAW OF COSINES: 2 a = b 2 = c 2 =

Use Law of Cosines to solve for Cos A.

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

Solve for all missing information …

EXAMPLE 1: Two ships leave at 4 pm. 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 6 pm?

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?