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Trigonometry, 2ADV T1 2016 HSC 12c

Square tiles of side length 20 cm are being used to tile a bathroom.

The tiler needs to drill a hole in one of the tiles at a point which is 8 cm from one corner and 15 cm from an adjacent corner.

To locate the point the tiler needs to know the size of the angle shown in the diagram.
 

 hsc-2016-12c

 
Find the size of the angle to the nearest degree.  (3 marks)

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α

 

 

 
 

Trigonometry, 2ADV T1 2015 HSC 13a

The diagram shows with sides  cm, cm  and  cm.
 

  1. Show that  .  (1 mark)

  2. By finding the exact value of , determine the exact value of the area of  .  (2 marks)

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  2. ²
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i. 

 
 
 
 

 

♦ Mean mark 40%.
ii.    2UA HSC 2015 13ai

 

 
  ²

Trigonometry, 2ADV T1 2006 HSC 4a

In the diagram, represents a garden. The sector    has centre and 

The points and lie on a straight line and  metres.

Copy or trace the diagram into your writing booklet.

  1. Show that    (1 mark)

  2. Find the length of  .  (2 marks)

  3. Find the area of the garden  .  (2 marks)

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  3. ²
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i.   

π
 

 

 

 

ii. 

 
 
 

 

iii. 
 
 
  ²

 

²

 

²

Trigonometry, 2ADV T1 2005 HSC 3b

The lengths of the sides of a triangle are 7 cm, 8 cm and 13 cm.

  1. Find the size of the angle opposite the longest side.  (2 marks)

  2. Find the area of the triangle.  (1 marks)

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i.

 Trig Ratios, 2UA 2005 HSC 3b Answer1 

 

 

 

 

ii. 

 
 
 

Trigonometry, 2ADV T1 2011 HSC 8a

In the diagram, the shop at    is 20 kilometres across the bay from the post office at  . The distance from the shop to the lighthouse at    is 22 kilometres and    is 60°.

Let the distance    be    kilometres.
 

2011 8a
 

  1. Use the cosine rule to show that  .    (1 mark)

  2. Hence, find the distance from the post office to the lighthouse. Give your answer correct to the nearest kilometre.    (2 mark)

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i. 

  

 

ii. 

 
 
 
 

Trigonometry, 2ADV T1 2012 HSC 13a

The diagram shows a triangle  . The line    meets the  and  axes at the points  and  respectively. The point  has coordinates  . 
 

2012 13a
 

  1. Calculate the distance  .   (2 marks)

  2. It is known that    and  (Do NOT prove this)  

     

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

  3. The point lies on    such that    is perpendicular to  . 

     

    Find the coordinates of .    (3 marks)

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i.   

 


  

 
 
 

 

ii.   

   
 
 
 
 
 

 

iii. 

½

 

½

MARKER’S COMMENT: Many students could not find the correct equation on because they took its gradient to be the reciprocal of and not the negative reciprocal. 
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