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Trigonometry, 2ADV T1 2020 HSC 15

Mr Ali, Ms Brown and a group of students were camping at the site located at . Mr Ali walked with some of the students on a bearing of 035° for 7 km to location . Ms Brown, with the rest of the students, walked on a bearing of 100° for 9 km to location .
 


 

  1. Show that the angle is 65°.  (1 mark)

  2. Find the distance .  (2 marks)

  3. Find the bearing of Ms Brown's group from Mr Ali's group. Give your answer correct to the nearest degree.  (2 marks)

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a.   
   

 

b.   

 
 
 

 
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Trigonometry, 2ADV* T1 2011 HSC 24c

A ship sails 6 km from to on a bearing of 121°. It then sails 9 km to .  The
size of angle is 114°.
 

2UG 2011 24c

Copy the diagram into your writing booklet and show all the information on it.

  1. What is the bearing of from ?   (1 mark)

  2. Find the distance . Give your answer correct to the nearest kilometre.   (2 marks)

  3. What is the bearing of from ? Give your answer correct to the nearest degree.   (3 marks)

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  2.  
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Show Worked Solution
STRATEGY: This deserves repeating again: Draw North-South parallel lines through major points to make the angle calculations easier!
i.     2011 HSC 24c

 

 
 

   

 

ii.   

 
 
 

 

iii.   

MARKER’S COMMENT: The best responses showed clear working on the diagram.
 
 

 

 
 
 

Trigonometry, 2ADV* T1 2017 HSC 30c

The diagram shows the location of three schools. School is 5 km due north of school , school is 13 km from school and is 135°.
 


 

  1. Calculate the shortest distance from school to school , to the nearest kilometre.  (2 marks)

  2. Determine the bearing of school from school , to the nearest degree.  (3 marks)

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(i)  

 
 
 

 

(ii)   

♦♦ Mean mark part (ii) 31%.
 

 

Trigonometry, 2ADV* T1 2005 HSC 27c

2UG-2005-27c
 

The bearing of from is 250° and the distance of from is 36 km.

  1. Explain why    is  .   (1 mark)

  2. If    is 15 km due north of  , calculate the distance of    from  , correct to the nearest kilometre.   (3 marks)

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i. 

 

ii.   
 
 
 

Trigonometry, 2ADV* T1 2007 26a

The diagram shows information about the locations of towns  ,    and  .
 

 
 

  1. It takes Elina 2 hours and 48 minutes to walk directly from Town    to Town  .

     

    Calculate her walking speed correct to the nearest km/h.    (1 mark)

  2. Elina decides, instead, to walk to Town    from Town    and then to Town  .

     

    Find the distance from Town    to Town  . Give your answer to the nearest km.   (2 marks)

  3. Calculate the bearing of Town    from Town  .   (1 mark)

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i. 

 

 

 
 

 

ii.  

 
 

 

 

iii.  

 

Trigonometry, 2ADV* T1 2009 HSC 27b

A yacht race follows the triangular course shown in the diagram. The course from    to    is 1.8 km on a true bearing of 058°.

At    the course changes direction. The course from    to    is 2.7 km and  .
 

 2009-2UG-27b
 

  1. What is the bearing of    from  ?   (1 mark)

  2. What is the distance from    to  ?     (2 marks)

  3. The area inside this triangular course is set as a ‘no-go’ zone for other boats while the race is on.

     

    What is the area of this ‘no-go’ zone?   (1 mark)

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  3. ²
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i.    2UG-2009-27b-Answer

TIP: Draw North-South parallel lines through relevant points to help calculate angles as shown in the Worked Solutions.

 

(ii)   

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(iii)   

 
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Trigonometry, 2ADV* T1 2014 HSC 23 MC

The following information is given about the locations of three towns , and : 
 

• is due east of 

• is on a bearing of    from   

• is on a bearing of    from  . 

 
Which diagram best represents this information?
 

HSC 2014 23mci

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COMMENT: Drawing a parallel North/South line through makes this question much simpler to solve.


 

 


 

Trigonometry, 2ADV T1 2018 HSC 12a

A ship travels from Port A on a bearing of 050° for 320 km to Port B. It then travels on a bearing of 120° for 190 km to Port C.
 


 

  1. What is the size of  ?  (1 mark)

  2. What is the distance from Port A to Port C ? Answer to the nearest 10 kilometres.  (2 marks)

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i.  

 

 

ii. 

 
 
 

Trigonometry, 2ADV T1 2004 HSC 3c

Trig Ratios, 2UA 2004 HSC 3c
 

The diagram shows a point    which is  30 km due west of the point  .

The point    is 12 km from    and has a bearing from    of  070°. 

  1. Find the distance of    from  .   (2 marks)

  2. Find the bearing of    from  .   (2 marks)

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i.   

Trig Ratios, 2UA 2004 HSC 3c Answer

 
 
 

 

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Trigonometry, 2ADV T1 2014 HSC 13d

Chris leaves island    in a boat and sails 142 km on a bearing of 078° to island  .  Chris then sails on a bearing of 191° for 220 km to island  , as shown in the diagram.
 

 

  1. Show that the distance from island    to island    is approximately 210 km.    (2 marks)

  2. Chris wants to sail from island    directly to island  . On what bearing should Chris sail? Give your answer correct to the nearest degree.    (3 marks)

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i.   

 


 

 

 

 
 
 

 

ii.