Dr. J's Maths.com
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Trigonometry - Bearings and Trig. Rules.
Test Yourself 1.


 

Using the sine rule 1. In a large park at the bottom of my hill, is a large recreational area with a lagoon.

From where I am standing, I notice an Australian Wood Duck about 180 m away on a bearing of 220°. I also notice a flock of similar ducks - all close to one another - about 100 m away on a bearing of 155°.
Source: Australian Museum.
 
(i) Show that the angle through which I must move my eyes from the single Wood Duck to the flock is 65°.

(ii) How far away is the single Wood Duck from the flock?

(iii) On what bearing should the single Wood Duck fly to join the flock?
  2.
 

Three ports A, B and C are reasonably close together. Port B is on a bearing of 250° from Port A while Port C is on a bearing of 240° from Port A.

Port C is 100 km east of Port B.

(i) Draw a digram to show the information provided.

(ii) A pleasure cruiser leaves Port A at 10 am and travels at 30 kph directly towards Port B. At what time does it arrive at Port B?

(iii) A Whale Watcher cruiser leaves Port A to go directly to Port C one hour after the pleasure cruiser. At what speed should the Whale Watcher travel if it arrives at Port C at the same time as the pleasure cruiser arrives at Port B?
   
  CK nautical miles
Using the cosine rule.

6. Ship A is 20 nautical miles away from Port P and is on a bearing of 55°.

Ship B is 27 nautical miles from P and is on a bearing of 115°.

(i) Draw a diagram showing the relevant information.

(ii) Show that the angle between Ship A, the Port and Ship B is 60°.

(iii) Use the cosine rule to determine the distance between the two ships giving your answer to the nearest nautical mile.

 
 

7. The diagram below describes the path of a ship which leaves a Port at A on a course of 075o for 20 kilometres. When the ship reaches point B off a headland, it changes course to 130o and continues sailing for 30 kilometres to the Port at C.

(i) Show <ABC = 125o.

(ii) How far, in a direct line from its starting point, is the ship when it is in Port C?

(iii) What is the bearing of Port C from Port A?
 

A Team Leader mapped out an orienteering course for the a group of beginners. She left point from B on a bearing of 050° and walked for 7 km and placed a marker N. From point N she
walked on a bearing of 120° and walked for 8 km to a point E.

(i) Draw a diagram to represent this information.

(ii) Show that the angle BNE = 110°.

(iii) What is the distance back to the base camp B from E (to the nearest 100 m)?

(iv) What is the bearing of A from C (nearest degree)?

Answer.(iii) BE = 12.3 km.
(iv) Bearing of A from E is 268°.
 

 
 

 
Using both cosine and sine rules.  
   
   
Bearings with other rules.

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.

Calculate the distance between the ships (to 1 decimal place).