Navigation Trig Day 3 Notes

Pre-Calculus Right Triangle Trig Navigation Applications NOTES Name The course of a ship or plane is the angle, measured _______________________________, from the _________________________________________________________ to the direction of the ship or the plane. This “course” is called a ___________________________, and is denoted using _______________digits. BEARING: Example 1: Given the NORTH-SOUTH lines, draw the following bearings: Bearing of 100° Bearing of 065° Bearing of 210° Bearing of 320° Sometimes, the bearing is described using _____________________________ instead of just saying “bearing.” The 1st letter is the direction in which you_______________, the 2nd letter is the direction in which you _______. Also, you typically start with _____________ or _____________ then move _____________ or _____________. Example 2: Given the NORTH-SOUTH lines, draw the following bearings: 𝑁 15° 𝐸 𝑆 105° 𝑊 𝑆 280° 𝐸 𝑁 75° 𝑊 Name these another way, using 𝑆 instead of 𝑁, and vice versa. __________ __________ __________ __________ Sometimes, a degree measure is NOT given, and the direction is implied. Example 3: Given the NORTH-SOUTH lines, draw the following bearings: Northeast Southwest Proceeds South Proceeds West __________ __________ What is the bearing for each of the above courses? __________ __________ NAUTICAL MILE: 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.? 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 form its point of departure. 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? ***************************************************************************** Pre-Calculus Right Triangle Trig Navigation Applications HOMEWORK Name Dec. 2014 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° 7. 𝑁 170° 𝐸 8. 𝑆 100° 𝐸 Given the NORTH-SOUTH lines, draw the following bearings: 5. 𝑁 35° 𝑊 6. 𝑆 20° 𝑊 Given the NORTH-SOUTH lines, draw the following bearings: 9. Northwest 10. Proceeds East 11. Southeast 12. South 15. __________ 16. __________ What is the bearing for each of the above courses? 13. __________ 14. __________ For each of the following, draw a picture and then obtain the desired information. 17. A ship leaves port at noon and has a bearing of 𝑆 34° 𝐸. The ship sails at 30 knots. How many nautical miles south and how many nautical miles east will the ship have travelled by 4:00 p.m.? 18. A fisherman leaves his home port and heads in the direction 𝑁 70° 𝑊. He travels 30 miles. How far north and how far west is he from his home port? 19. A ship leaves port at 10:00 a.m. and has a bearing of 𝑁 16° 𝐸. The ship sails at 25 knots. How many nautical miles north and how many nautical miles east will the ship have travelled by 2:30 p.m.? 20. A plane is 160 miles north and 85 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should be taken? 21. A ship is 70 miles east and 40 miles south of port. The captain wants to sail directly to port. What bearing should be taken? 22. An airplane flies on a course of 110° at a speed of 1200 km/hr. How far east of its starting point is it after 2 hours? 23. An ship sails on a course of 304° at a speed of 50 knots. How far west of its starting point is it after 4 hours? 24. A hunter walks east for 1 hour and then north for 1.5 hours. What course should the hunter take to return to his starting point? 17. 67.1 nm east; 99.5 nm south 18. 10.3 miles north; 28.2 miles west 19. 31.0 nm east; 108.1 nm north 20. 207.98° or 𝑆 27.98° 𝑊 21. 299.77° or 𝑁 60.3° 𝑊 22. 2255.26 km 23. 165.8 nm west 24. 213.7° or 𝑆 33.7° 𝑊