Bearings

(1) A small boat leaves a harbour H and travels due East (bearing 090 degrees) for 40 km to a marker buoy B and then sails directly towards a lighthouse L which is 24 km from B. It then returns to the harbour H, that is a distance of 57 km on a bearing of 250^o.

Either by a scale drawing, or using trigonometry, find the bearing of the lighthouse L from the buoy B (the angle marked with a ? mark in the diagram).

Note: A bearing is the angle, measured in the clockwise direction, between the north south direction and a line connecting two points. Bearings are always given by 3 figures. For example, in the diagram, the bearing of L from H is 070^o and the bearing of H from L is 250^o.

(2) Two observers P and Q on a beach, standing 100 metres apart, see a shark not far from the beach and they need to warn swimmers. Observer P sights the shark on a bearing 070^o and observer Q sights it on a bearing 320^o. How far is the shark from the beach?

Click here for the Notes for Teachers.

Click here for the BEARINGS worksheet.