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Measurement, STD2 M6 2023 HSC 27

The diagram shows the location of three places , and .

is on a bearing of 120° and 15 km from .

is 40 km from and lies due west of .

lies on the line joining and and is due south of .
  

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

  2. What is the bearing of from , to the nearest degree?  (2 marks)

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a.   

 
 
   

 
b.   

 
 
   
   

 

 
   

♦ Mean mark (b) 39%.

Measurement, STD2 M6 2022 HSC 33

The diagram shows an aeroplane that was flying towards an airport at  on a bearing of . When it was at point , 20 km away from the airport at  , the flight course was changed. The aeroplane landed at an airport at directly south of . The distance from to is 50 km.
 


 

  1. Show that the distance between the airport at  and the airport at is 38.5 km, correct to 1 decimal place.  (2 marks)

  2. Use the sine rule to find the angle to the nearest degree.  (2 marks)

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

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a.   
 

 
   
 
   

♦ Mean mark part (a) 50%.

 

b.   

 
 
 
   
   

♦♦ Mean mark part (b) 39%.

 

c. 


♦♦ Mean mark part (c) 25%.

Measurement, STD2 M6 2020 HSC 31

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.   

Mean mark 53%.
 
 
 

 
c.

 

♦♦ Mean mark 22%.

 
   
 
   

 

 

Measurement, STD2 M6 SM-Bank 4

The diagram shows three checkpoints A, B and C. Checkpoint C is due east of Checkpoint A. The bearing of Checkpoint B from Checkpoint A is N22°E and the bearing of Checkpoint C from Checkpoint B is S68°E. The distance between Checkpoint A and Checkpoint B is 42 kilometres.
 


 

  1. Mark the given information on the diagram and explain why is 90°.  (2 marks)

  2. Find the distance, to the nearest kilometre, between Checkpoint A and Checkpoint C.  (2 marks)

  3. If a runner is travelling 12.6 km/h, how long does it take her to travel between Checkpoint A and Checkpoint B, in hours and minutes?  (2 marks)

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i.   
 

 

ii.  

 
 

 

iii.   
   
   
   

Measurement, STD2 M6 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°.
 

  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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  1.  
  2.  
  3.  
Show Worked Solution
STRATEGY: Important: 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 clearly showed what steps were taken with working on the diagram. Note that all North/South lines are parallel.
 
 

 

 
 
 

Measurement, STD2 M6 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 31%.
 

 

Measurement, STD2 M6 2005 HSC 27c

2UG-2005-27c
 

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

  1. Explain why    is 110°.   (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.   
 
 
 

Measurement, STD2 M6 2007 HSC 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  

 

Measurement, STD2 M6 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  145°  from   

• is on a bearing of  060°  from  . 

Which diagram best represents this information?
 

HSC 2014 23mci

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♦ Mean mark 38%
COMMENT: Drawing a parallel North/South line through makes this question much simpler to solve.


 

 

Measurement, STD2 M6 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
Show Worked Solution
i.    2UG-2009-27b-Answer

♦♦♦ Mean mark 18%.
TIP: Draw North-South parallel lines through relevant points to help calculate angles as shown in the Worked Solutions.

 

ii.   

♦ Mean mark 36%
 +  
   +  
 
 
 
 

 

iii.  

♦ Mean mark 44%
 
  ²

 

²