L1 Mathematical Reasoning
Question Bank
A tramper walks 5 km from her campsite on a bearing of 135°.
Calculate how far South and how far East she has travelled from her starting point.
The keeper of a lighthouse spots a ship on a bearing of 295°.
What is the bearing of the lighthouse from the ship?
An air traffic controller at an airport control tower (P) is tracking two planes. Plane A is on a bearing of 040° and Plane B is on a bearing of 115°.
What is the angle between the two planes from the perspective of the control tower ($\angle APB$)?
A kayaker paddles 4 km due South from a wharf, then turns and paddles 3 km due West to a beach.
What is the bearing of the wharf from the beach?
Two rescue boats leave the same port at the same time to search for a distress flare.
Boat A travels 90 km on a bearing of 040°.
Boat B travels 120 km on a bearing of 130°.
(i) Find the direct distance between the two boats.
(ii) Find the bearing of Boat A from Boat B, shown as angle 'y' in the diagram.
A treasure map says to go from the old oak tree (O) 50m on a bearing of 060° to a rock (R). From the rock, you must walk 40m due North to find the treasure (T), as represented in the diagram.
Calculate the direct distance from the old oak tree to the treasure.
A ship sails from Port A for 100 km on a bearing of 120°. It then changes course and sails for 150 km on a bearing of 220° to reach Port C. The ship's path is represented by the basic triangle in the diagram below.
Calculate the bearing of Port A from Port C.
A hiker (H) is in a park and can see two towers, T1 and T2, which she knows are on a straight east-west track 20 km apart. From the hiker's position, the bearing to tower T1 is 315°, and the bearing to tower T2 is 45°.
Calculate the shortest distance from the hiker to the track. You must fully justify your answer.