University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2021
Views:

65

Pages:

6
Author:

GalacticGuru

Navigation Applications Notes The course of a ship or plane is the angle, measured clockwise from the north direction to the direction of the ship or plane. This "course" is called a bearing. BEARING: A bearing measures the acute angle a path or line of sight makes with a fixed north-south line. Example 1: Given the NORTH-SOUTH lines, draw the following bearings: four diagrams showing bearings of 100°, 065°, 210°, and 320° Bearing of 100° Bearing of 065° Bearing of 210° Bearing of 320° Sometimes, the bearing is described using north-south-east-west instead of just saying "bearing." The 1st letter is the direction in which you start (north or south) The 2nd letter is the direction in which you go (east or west) Example 2: Given the NORTH-SOUTH lines, draw the following bearings: four diagrams showing bearings of N 15° E, S 105° W, S 280° E, N 75° W N 15° E S 105° W S 280° E N 75° W Name these another way, using S instead of N, and vice versa. S 165° E N 255° W N 80° E S 105° W Sometimes, a degree measure is NOT given, and the direction is implied. Example 3: Given the NORTH-SOUTH lines, draw the following bearings: What is the bearing for each of the above courses? Northeast: 045° Southwest: 225° Proceeds South: 180° Proceeds West: 270° NAUTICAL MILE: * Distance at Sea or in the air * Knots x time = n.m. Example 4: Draw the diagram first, then obtain the desired information. A ship leaves port at noon and has a bearing of S 29° W. The ship sails at 20 knots. How many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 p.m.? distance = 20 x 6 = 120 cos 61° = W/120 sin 61° = S/120 W = 58.2 nm S = 105.0 nm Example 5: Draw the diagram first, then obtain the desired information. An airplane flying at 600 miles per hour has a bearing of 52°. After flying for 1.5 hours, how far north and how far east has the plane traveled from its point of departure? 600 x 1.5 = 900 miles cos 38° = e/900 sin 38° = n/900 e = 709.2 miles n = 554.1 miles Example 6: Draw the diagram first, then obtain the desired information. A ship is 45 miles east and 30 miles south of port. (Hint: place "Port" at the origin") The captain wants to sail directly to port. What bearing should be taken? tanθ = 45/30 θ = 56.31° N 56.31° W or a bearing of 303.69° Pre-Calculus Navigation Applications Right Triangle Trig HOMEWORK Given the NORTH-SOUTH lines, draw the following bearings: 1. Bearing of 120° 2. Bearing of 030° 3. Bearing of 250° 4. Bearing of 310° Given the NORTH-SOUTH lines, draw the following bearings: 5. N 55° W 6. S 20° W 7. N 170° E 8. S 100° E