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Measurement, STD2 M6 2020 HSC 32

The diagram shows a regular decagon (ten-sided shape with all sides equal and all interior angles equal). The decagon has centre .
 

The perimeter of the shape is 80 cm.

By considering triangle , calculate the area of the ten-sided shape. Give your answer in square centimetres correct to one decimal place.  (4 marks)

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²

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♦♦ Mean mark 33%.


 

 

 
  ²

Measurement, STD2 M6 2020 HSC 16

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)

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a.     
 
   
   

 

b.     

 
 

Measurement, STD2 M6 2019 HSC 12 MC

An owl is 7 metres above ground level, in a tree. The owl sees a mouse on the ground at an angle of depression of 32°.

How far must the owl fly in a straight line to catch the mouse, assuming the mouse does not move?

  1.  3.7 m
  2.  5.9 m
  3.  8.3 m
  4.  13.2 m
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♦ Mean mark 36%.

 

 

Measurement, STD2 M6 2019 HSC 22

Two right-angled triangles, and , are shown.
 

Calculate the size of angle , correct to the nearest minute.  (3 marks)

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Mean mark 51%.

 

 

 
 
 

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)

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Measurement, STD2 M6 2017 HSC 8 MC

The diagram shows a right-angled triangle.
 


 

What is the value of  , to the nearest minute?

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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?

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♦ 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)

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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
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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
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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)

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♦♦ 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)

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i.   

ii.   

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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)

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♦♦ 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 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
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