Objective: Solve real-life problems involving directional bearing Bearings Objective: Solve real-life problems involving directional bearing

Bearing In surveying and navigation, directions can be given in terms of bearings. A bearing measures the acute angle that a path or line of sight makes with a fixed north- south line. FIRST TYPE: a single angle measured in a clockwise direction from due north SECOND TYPE: expressing bearing that starts with a north-south line and uses an acute angle to show the direction either east or west from this line

Bearing The problems will result in right triangles. Start each problem by drawing a sketch. It would be foolish to attempt to solve the problem without drawing a sketch. The importance of a correctly labeled sketch in applications such as this cannot be overemphasized, as some of the necessary information is often not given in the problem and can only be determined from the sketch.

Example of first type of bearing 1. Radar stations A and B are on an east-west line, 3.7 kilometers apart. Station A detects a plane at C, on a bearing of . Station B simultaneously detects the same plane, on a bearing of . Find the distance from A to C

Example of second type of bearing 2. The bearing from A to C is . The bearing from A to B is . The bearing from B to C is . A plane flying at 250 miles per hour takes 2.4 hours to go from A to B. Find the distance from A to C

Finding directions in terms of bearings 3. A ship leaves port at noon and heads due west at 20 knots, or 20 nautical miles per hour. At 2 P.M. the ship changes course to . Find the ship’s bearing and distance from the port of departure at 3 P.M.