Trig - bearings TYS 1

Conversions from compass to true bearings.	1. Convert the following compass bearings to true bearings:
	(i) South (ii) West (iii) North west (iv) North east.	(v) North north east (NNE) (vi) West south west (vii) East 25° south (viii) West 15° north
Conversions from true to compass bearings.	2. Convert the following true bearings to compass bearings:
	(i) 0° T. (ii) 270° T. (iii) 135° T. (iv) 020° T.	(v) 210° T. (vi) 310° T. (vii) 157.5°. (viii) 202.5°.
Bearings "looking back" FROM	3. The compass bearing of Point A from Point B is N38°E. (i) Draw that information on a diagram. (ii) What is the bearing of Point B from Point A? Answer.Bearing of B is S38°W from A or W52°S.
	4. A ship sails from Point A at a bearing of 090° to point B. It then changes bearing and sails along a course at 240°. What will be the bearing of the ship from point A when the ship travelling on its new course is at its closest distance to point A? Answer.Bearing of 150° from A.
	5. The compass bearing of A from B is S42°E. What is the compass bearing from B to A? Answer.Bearing from B to A is N42°W or W48°N.
	6.
Bearings in right angle triangles.	7. A ship travels 150 km in a north 40° west direction. (i) How far north of the starting point is the ship? (ii) How far west of the starting point is the ship? Answer to the nearest km. Answer.(i)North: 115 km. (ii) West: 96 km.




Bearings with other rules.	11. A ship S sails from port P on a bearing of N 60° E for 56 kms. Another ship A also leaves port P but on a bearing 110° T for 48 kms. (i) Draw a diagram to reflect this information. (ii) Calculate the distance between the ships (to 1 decimal place).
	12. Three ships start from Port O. Ship A sails at 60 nautical miles per hour at a bearing of 342°; Ship B sails at 40 nautical miles per hour at a bearing of 128°; Ship C sails at 30 nautical miles per hour at a bearing of 058°. (i) Draw a diagram to indicate the position of each ship after 45 minutes have elapsed. (ii) Calculate the distance of Ship B from Ship A; (iii) Find the bearing of ship C from Ship B. Answer.(ii) AB = 72 nm. (ii) Bearing of C from B is 338°T.
	13. The diagram below shows three towns, A, W and B. A plane travelling from town A to town B must make a stop-over at town W. Town W is 120 km on a true bearing of 312° from town A. Town B, which is directly north of town A, is on a true bearing of 042° from town W. (i) Draw a diagram to represent this information about the relative location of the three towns. (ii) How much farther is the plane’s trip with the stop-over at W than if it were to fly directly from A to C? Express your answer to the nearest kilometre. Answer.(ii) 253 - 179 = 74 km.
	14. A course for a Championship Drone event requires competitors to fly from point A on a bearing of 050° for 1.2 km over cliffs with significant updrafts to point B. From point B they must then fly on a bearing of 230° over land for 2.8 km to point C. (i) Draw a diagram to represent this information. (ii) Find the distance from point C to point A, to the nearest 100 m. (iii) What is the bearing of C from A?
	15. I am looking at Curl Curl beach from a headland. I know that the beach faces east south-east and I draw a small sketch as shown below.
	(i) If I am standing on the beach and looking directly out at right angles to the beach, at what true bearing will I be looking? (ii) From my vantage point, I am looking directly down the length of the beach. What is my true bearing from the beach? (iii) What are the true bearing and the compass bearing from my vantage point directly down the beach?	Answer.(i) True bearing is 112.5°. (ii) Bearing to me FROM beach is 22.5°. (iii) Bearing of Beach from me is 202.5°T or S22.5°W. which is SSW.