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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 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 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.