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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)

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♦♦ Mean mark 30%.

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 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 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 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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