Multiple Choice

1. A hiker walks $5 \text{ km}$ on a bearing of $045^\circ$ from point A to point B, then $7 \text{ km}$ on a bearing of $150^\circ$ from point B to point C. What is the bearing of their final position (C) from their starting point (A)?

   $000.2^\circ$

   $134.8^\circ$

   $044.8^\circ$

   $089.8^\circ$

2. A boat sails from port P to buoy B, a distance of $12 \text{ km}$ on a bearing of $070^\circ$. From port P, a lighthouse L is on a bearing of $110^\circ$. If the distance from buoy B to lighthouse L is $8 \text{ km}$, what is the bearing from buoy B to lighthouse L?

   $245.5^\circ$

   $104.5^\circ$

   $034.6^\circ$

   $135.5^\circ$

3. Ship A leaves port on a bearing of $030^\circ$ at $20 \text{ km/h}$. Ship B leaves the same port 1 hour later on a bearing of $120^\circ$ at $25 \text{ km/h}$. What is the bearing of Ship B from Ship A, 2 hours after Ship A left port?

   $178.0^\circ$

   $242.0^\circ$

   $032.0^\circ$

   $088.0^\circ$

4. A plane flies from airport A to town B on a bearing of $060^\circ$ for $150 \text{ km}$. It then flies from town B to city C on a bearing of $135^\circ$ for $200 \text{ km}$. What is the bearing of city C from airport A?

   $183.0^\circ$

   $123.0^\circ$

   $063.0^\circ$

   $003.0^\circ$

5. From point X, a landmark Y is on a bearing of $055^\circ$. From the same point X, a landmark Z is on a bearing of $100^\circ$. If the distance from Y to Z is $30 \text{ km}$, and the bearing of Z from Y is $160^\circ$, what is the distance from X to Y?

   $25.9 \text{ km}$

   $21.2 \text{ km}$

   $15.0 \text{ km}$

   $30.0 \text{ km}$

6. A hiker walks $8 \text{ km}$ on a bearing of $270^\circ$ from point S, then $6 \text{ km}$ on a bearing of $000^\circ$. What bearing must the hiker take to return directly to the starting point S, and what is the distance?

   $053.1^\circ$, $10 \text{ km}$

   $143.1^\circ$, $10 \text{ km}$

   $323.1^\circ$, $10 \text{ km}$

   $233.1^\circ$, $10 \text{ km}$

7. Port A is $100 \text{ km}$ due North of Port B. A ship leaves Port A on a bearing of $130^\circ$ at $30 \text{ km/h}$. At the same time, another ship leaves Port B on a bearing of $060^\circ$ at $25 \text{ km/h}$. How far apart are the ships after $2$ hours?

   $36.5 \text{ km}$

   $55.0 \text{ km}$

   $42.1 \text{ km}$

   $29.8 \text{ km}$

8. A surveyor starts at point P, walks $100 \text{ m}$ on a bearing of $045^\circ$ to point Q, then $120 \text{ m}$ on a bearing of $300^\circ$ to point R. What is the bearing of point P from point R?

   $345.7^\circ$

   $194.3^\circ$

   $165.7^\circ$

   $014.3^\circ$

9. A lighthouse (L) is $50 \text{ km}$ from a port (P) on a bearing of $070^\circ$. A ship (S) is on a bearing of $100^\circ$ from P. The bearing of the ship (S) from the lighthouse (L) is $190^\circ$. What is the distance between the ship and the lighthouse?

   $25.0 \text{ km}$

   $30.0 \text{ km}$

   $43.3 \text{ km}$

   $50.0 \text{ km}$

10. A ship sails from port P on a bearing of $040^\circ$. After $30 \text{ km}$, it spots an island (I) on a bearing of $110^\circ$ from its current position (Q). The island I is known to be on a bearing of $080^\circ$ from the port P. What is the shortest distance from the island to the ship's initial path (line PQ)?

    $25.7 \text{ km}$

    $22.9 \text{ km}$

    $15.0 \text{ km}$

    $19.3 \text{ km}$