Alg 2 BC U12Day 11 – Bearing Problems
Bearing Type 1: N 34o W (Ex: Town A is at a bearing of N 34o W from Town B.)
Bearing Type 2: bearing of 164o
Ex: Town A is at a bearing of 164o from Town B.
Example 1: Radar stations A and B are on an east-west line, 3.7 kilometers apart. Station A detects a plane at another point C on a bearing of 61°. Station B simultaneously detects the same plane on a bearing of 331°. Find the distance from A to C.
Example 2: The bearing from A to C is S52°E. The bearing from A to B is N84°E. The bearing from B to C is S38°W. A plane flying 250 miles per hour takes 2.4 hours to go from A to B. Find the distance from A to C.
- A boat travels at a speed of 40 miles per hour from Ft.Lauderdale on a course of N65ºE for 2 hours, then changes to a course of S25ºE for 4 hours at the same speed. Determine the distance from Ft.Lauderdale to the boat.
2.The bearing from point A to point B is S 55° E and from point B to point C is N 35° E. If a ship sails from A to B a distance of 80 km, and then sails from B to C a distance of 74 km, how far is it from A to C?
3.A surveyor wishes to find the distance across a river. The bearings from 2 points 70 feet apart on the same bank of the river to a tree on the opposite bank are N and N34ºW. Find the width of the river.
4. Two towers are on a north-south line. From tower A, a ship is located on a bearing of 247 and from tower B, the bearing of the ship is 337. Find the distance between the towers if the distance from tower A to the ship is 2572 meters.
5.Two lighthouses are on an east-west line. From lighthouse C, a boat in distress is 15.4 miles away on a bearing of 328. From lighthouse D, the boat is on a bearing of 58. How far will a rescue boat have to travel from D to get to the boat?
6.A ship is sailing east. At one point the bearing of a submerged rock is at 45 degrees 20 minutes. The ship sails for 15.1 miles and then the rock is at a bearing of 315 degrees 20 minutes. What the distance of the rock at the later point?
Answers:
1. 178.885 mi2. 108.977 km 3. 103.779 ft 4. 6582.532 m 5. 24.645 mi 6. 10.615 mi
Some more challenging problems:
7. A ship leaves port and travels due west for 30 nautical miles, then changes course to S30ºW and travels 40 more nautical miles. Find the bearing from the ship to the port of departure and from the port of departure to the ship.
8. Two ships A and B sight a distress flare, F, that is 130 km from A and 104 km from B. Ship A sights the flare at a bearing of 175°. Ship B sights the flare at a bearing of 225°. If the bearing of ship A from ship B is 315°, how far apart are the ships?
9. A ship leaves at noon and heads due west at 20 knots, or20 nautical miles per hour. At 2 p.m. the ship changescourse toN 54° W. Find the ship’s bearing and distance from the port of departure at 3 p.m.
Answers:
7. bearing from ship: 55.285°, bearing from port: 205.285°
8. 78 km
9. 57.397 mi, bearing 281.819°