SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Measurement, STD1 M3 2023 HSC 29

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)

Show Answers Only
Show Worked Solution

a.   

 
 
   

♦♦ Mean mark (a) 24%.

b.   

 
 
   
   

 

 
   

♦♦♦♦ Mean mark (b) 9%.

Measurement, STD1 M3 2023 HSC 16

From the top of a vertical cliff 120 metres high, a boat is observed. The angle of depression of the boat from the top of the cliff is 18°, as shown in the diagram.
 

Find the distance of the boat from the base of the cliff. Give your answer to the nearest metre.  (2 marks)

Show Answers Only

Show Worked Solution

 
 

♦♦ Mean mark 30%.

Measurement, STD1 M3 2021 HSC 28

A right-angled triangle is shown. The length of is 16 cm and .
 


 

  1. Find the side length, , of the triangle in centimetres, correct to two decimal places.  (2 marks)

  2. Hence, find the area of triangle in square centimetres, correct to one decimal place.  (3 marks)

Show Answers Only
Show Worked Solution
♦♦ Mean mark part (a) 24%.
a.   
 
   
   

 

b. 

♦♦♦ Mean mark part (b) 14%.
 
   
   
   

Measurement, STD1 M3 2020 HSC 11

Consider the triangle shown.
 


 

  1. Find the value of , correct to the nearest degree.   (2 marks)

  2. Find the value of , correct to one decimal place.   (2 marks)

Show Answers Only
Show Worked Solution
a.     
 
   
   

♦ Mean mark 44% and 39% for part (a) and (b) respectively.

 

b.     

 
 

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)

Show Answers Only
Show Worked Solution
i.   
 

 

ii.  

 
 

 

iii.   
   
   
   

Measurement, STD2 M6 2017 HSC 26d

A sewer pipe needs to be placed into the ground so that it has a 2° angle of depression. The length of the pipe is 15 000 mm.
 


 

How much deeper should one end of the pipe be compared to the other end? Answer to the nearest mm.  (2 marks)

Show Answers Only

Show Worked Solution

 
 

Measurement, STD2 M6 2017 HSC 8 MC

The diagram shows a right-angled triangle.
 


 

What is the value of  , to the nearest minute?

Show Answers Only

Show Worked Solution
 
 
COMMENT: An angle that has over 30″ (seconds) is rounded up to the next minute (i.e. rounded up to 70°17′).

 

 
 

 

Measurement, STD2 M6 2015 HSC 9 MC

From the top of a cliff 67 metres above sea level, the angle of depression of a buoy is 42°.
  

 

How far is the buoy from the base of the cliff, to the nearest metre?

Show Answers Only

Show Worked Solution
♦ Mean mark 49%.
COMMENT: The angle of depression is a regularly examined concept. Make sure you know exactly what it refers to.

 

Measurement, STD2 M6 2005 HSC 25b

2UG-2005-25b

  1. Use Pythagoras’ theorem to show that is a right-angled triangle.  (1 mark)

  2. Calculate the size of to the nearest minute.  (2 marks)

Show Answers Only
Show Worked Solution

i.   

 
 
 

MARKER’S COMMENT: Know your calculator process for producing an angle in minutes/seconds. Note >30 “seconds” rounds up to the higher “minute”.

 
ii. 

 
 

Measurement, STD2 M6 2006 HSC 3 MC

The angle of depression of the base of the tree from the top of the building is 65°. The height of the building is 30 m.

How far away is the base of the tree from the building, correct to one decimal place?
 


 

  1. 12.7 m
  2. 14.0 m
  3. 33.1 m
  4. 64.3 m
Show Answers Only

Show Worked Solution
 

 
 
   

 

Measurement, STD2 M6 2008 HSC 14 MC

Danni is flying a kite that is attached to a string of length 80 metres. The string makes an angle of 55° with the horizontal.

How high, to the nearest metre, is the kite above Danni’s hand?
 

VCAA 2008 14 mc
 

  1.    46 m
  2. 66 m
  3. 98 m
  4. 114 m
Show Answers Only

Show Worked Solution

2UG 2008 14MC ans

 

Measurement, STD2 M6 2010 HSC 24d

The base of a lighthouse, , is at the top of a cliff 168 metres above sea level. The angle of depression from to a boat at is 28°. The boat heads towards the base of the cliff, , and stops at . The distance is 126 metres.
 

  1. What is the angle of depression from to , correct to the nearest degree?   (3 marks)

  2. How far did the boat travel from to , correct to the nearest metre?   (2 marks)

Show Answers Only
Show Worked Solution
♦♦ Mean mark 31%
i.   
 
     

 

 
 

 

ii.     

♦♦ Mean mark 31%
MARKER’S COMMENT: Solve efficiently by using right-angled trigonometry. Many students used non-right angled trig, adding to the calculations and the difficulty.
 
 

 

 
 
 

Measurement, STD2 M6 2009 HSC 23a

The point is 25 m from the base of a building. The angle of elevation from  to the top of the building is 38°.
 

  1. Show that the height of the building is approximately 19.5 m.   (1 mark)

  2. A car is parked 62 m from the base of the building.

     

    What is the angle of depression from the top of the building to the car?

     

    Give your answer to the nearest minute.   (2 marks)

Show Answers Only

i.   

ii.   

Show Worked Solution

i. 

 
 

 

ii.  

♦♦ Mean mark 33%
MARKER’S COMMENT: If >30 “seconds”, round to the higher “minute”.
 
 
 
 

 

Measurement, STD2 M6 2012 HSC 27d

A disability ramp is to be constructed to replace steps, as shown in the diagram.

The angle of inclination for the ramp is to be 5°.   
  

Calculate the extra distance, , that the ramp will extend beyond the bottom step.

Give your answer to the nearest centimetre.   (3 marks)

Show Answers Only

 

Show Worked Solution

♦♦ Mean mark 35%
MARKER’S COMMENT:  The better responses used a diagram of a simplified version of the ramp as per the Worked Solution.
 
   
 
 

Measurement, STD2 M6 2011 HSC 9 MC

Two trees on level ground, 12 metres apart, are joined by a cable. It is attached 2 metres above the ground to one tree and 11 metres above the ground to the other.

What is the length of the cable between the two trees, correct to the nearest metre? 

  1.  
Show Answers Only

Show Worked Solution

 
 

 

Measurement, STD2 M6 2011 HSC 4 MC

The angle of depression from a kookaburra’s feet to a worm on the ground is 40°. The worm is 15 metres from a point on the ground directly below the kookaburra’s feet. 
 

 How high above the ground are the kookaburra's feet, correct to the nearest metre?

  1. 10 m
  2. 11 m
  3. 13 m
  4. 18 m
Show Answers Only

Show Worked Solution