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Trigonometry – Bearings 1. Amanda and Michael leave the same campsite and set off in different directions. Michael walks 7 kilometres on a bearing of 0350 and Amanda walks 8 kilometres due east. How far apart are Amanda and Michael? 2. Two yachts leave harbour H. Yacht A sails on a bearing of 0720 for 30 km and then stops. Yacht B sails on a bearing of 1400 for 50 km and then stops H How far apart are the two yachts when they both have stopped? 3. Debbie is taking part in an orienteering walk. She leaves checkpoint A and walks 6.8 km due south to checkpoint B. From B she walks 4.7 km on a bearing of 0800. How far is Debbie from checkpoint A? 4. Mark and Rabnawaz leave a hostel at the same time. Mark walks on a bearing of 0450 at a speed of 4.4 kmph. Rabnawaz walks on a bearing of 1000 at a speed of 4.8 kmph. If both walk at steady speeds, how far apart will they be after 2 hours? N 0 35 Amanda Michael 7 km 8 km 50 km 30 km B A N Rabnawaz Mark N 5. The sketch below shows the journey of a ship from a harbour. The ship leaves the harbour and sails 30 km on a bearing of 0400 and then sails 50 km on a bearing of 1000. Calculate the distance the ship is from the harbour. 6. Two ships leave Liverpool at the same time. One of them travels north-west at an average speed of 10.5 kmph while the other travels at an average speed of 14 kmph on a bearing of 2800. How far apart are these ships after 3 hours? 7. Three oil platforms, Alpha, Beta and Gamma are situated in the North Sea. Beta is 12 km from Alpha and is on a bearing of 1450 from Alpha. Gamma is 16 km from Alpha and is on a bearing of 2200 from Alpha. Find the distance of Beta from Gamma. 30 km 50 km 0 40 0 100 Harbour N N Alpha Beta Gamma N 12 km 16 km 8. A submarine is positioned at A. Its radar detects another ship 50 km away on a bearing of 1450, at C. The submarine informs its base at B, 40 km away on a bearing of 2100, of this ship. The base informs the submarine to intercept this ship. How far is the ship at C from the base B? 9. David takes part in a cross-country race. He leaves the starting point of the race David and runs due west for 5.5 km before changing direction and running 6.3 km in a north-west direction. Calculate how far David is from the starting point. 10. The diagram shows the position of 3 airports, A, E and G. G is 200km from A. E is 160 km from A From G the bearing of A is 0520. From A the bearing of E is 2160. How far apart are airports G and E? 11. The diagram shows the position of 3 towns E, B and F. B is 300 km from E and is on a bearing of 0460 from E. From E, the bearing of F is 1160. F is due south of B. Calculate the distance from E to F. 40 km 50 km B C A N 0 210 0 210 N N 5.5 km 6.3 km Start 200 km 160 km E G A N N E F B 300 km N N 12. A submarine leaves Faslane in Scotland and sails into the Atlantic Ocean on a bearing of 2500 for a distance of 120 km before changing course and sailing on a bearing of 1900 for 90 km. Calculate the distance the submarine is from Faslane. 13. An aeroplane flying to Edinburgh is 100 km due south of Edinburgh when the pilot is told to change direction because of fog. He is told to fly to Prestwick on a bearing of 3200. The bearing of Prestwick from Edinburgh is 2400. (a) Find the distance of the aeroplane from Prestwick. (b) Find the bearing of Edinburgh from Prestwick. 14. A church is 600 metres due west of a flagpole. A statue is on a bearing of 1600 from the church and on a bearing of 2200 from the flagpole. Find the distance of the church from the statue. Faslane N N 0 250 0 190 120 km 90 km N Edinburgh 100 km Prestwick Aeroplane 600 m 15. Three radio masts, K, W and P are situated in the Australian outback. K is 250km due south of W. W is 410km from P. P is on a bearing of 130° from K. Calculate the bearing of P from W. 16. A ship sails from harbour H on a bearing of 084° for 340km until it reaches point P. It then sails on a bearing of 210° for 160km until it reaches point Q. Calculate the distance between the point Q and the harbour. 17. Two ships A and B are anchored at sea. B is 65km due east of A. A lighthouse is positioned on a bearing of 055° from A and on a bearing of 310° from B. Calculate how far the lighthouse is from ship B. 410 km 250 km P K W N 0 130 Q P H N N 160 km 340 km 0 84 0 210 18. A ship, at position P, observes a lighthouse at position Q on a bearing of 040°. The ship travels 30km on a bearing of 125° to position R. From position R, the ship observes the lighthouse on a bearing of 340°. (a) Find the bearing of R from the lighthouse. (b) Calculate the distance from R to the lighthouse 19. A boat sails on a bearing of 160° for 600km before changing course and sailing 700km on a bearing of 050°. (a) How far the boat is from its starting point? (b) Find the bearing the ship is from its starting point. 20. A surveyor is walking due west when he comes to a marsh. To avoid the marsh he turns at P and walks for 60m on a bearing of 215° and then for 85m on a bearing of 290°. Calculate PR the direct distance across the marsh. 30 km N N R Q P 0 40 N 85 m 60 m N 0 215 0 290 R P Trig Worksheet – Bearings There are two ways to express a navigational heading or a “bearing”. 1. When a single angle is given, it is understood that the bearing is measured in a clockwise direction from due north. The bearing from A to C is 30 . C 30 A 2. The other system starts with a north or south line and uses an acute angle to show direction. The bearing from A to C is S 520 E (52 East of South) A 52 C South Give a diagram that represents each bearing. 1. bearing of 320 2. bearing of 3040 3. N 420 E 4. S 310 E 5. N 520 W Use these methods to draw a diagram to help you solve the following problems. Problem 1: A ship travels 70 km on a bearing of 270, and then travels on a bearing of 1470 for 180 km. Find the distance of the end of the trip from the starting point. Problem 2: Two lighthouses are located on a north-south line. From lighthouse A the bearing of a ship 3742 m away is 1290 43’. From lighthouse B the bearing of the ship is 390 43’. Find the distance between the lighthouses. Problem 3: Radio direction finders are set up at points A and B, which are 2.00 mi. apart on an east-west line. From A it is found that the bearing of the signal from a radio transmitter is N 360 20’ E, while from B the bearing of the same signal is N 430 40’ W. Find the distance of the transmitter from B. Problem 4: Radar stations A and B are on an east-west line, 3.7 miles apart. Station A detects a plane at C, on a bearing of 610. Station B detects the plane at a bearing of 3210. Find the distance from A to C.

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