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Trigonometry, 2ADV T1 2021 HSC 12

A right-angled triangle    is cut out from a semicircle with centre . The length of the diameter    is 16 cm and    = 30°, as shown on the diagram.
 


 

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

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

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a.   
 
   
   

 

b.   
   
   

 

 
   
   

 

 
   
   

Trigonometry, 2ADV T1 2018 HSC 14a

In    has length 3, has length 6 and is 60°. The point is chosen on side    so that    bisects . The length    is .
 


 

  1. Find the exact value of the area of  .  (1 mark)

  2. Hence, or otherwise, find the exact value of .  (2 marks)

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i.   

  ²

 

ii. 

♦ Mean mark 37%.

 

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 2009 HSC 5c

The diagram shows a circle with centre and radius 2 centimetres. The points    and    lie on the circumference of the circle and  .
 

2009 5c  
 

  1. There are two possible values of    for which the area of    is    square centimetres. One value is  .

     

    Find the other value.    (2 marks)

  2. Suppose that  .

     

    (1)  Find the area of sector     (1 mark)

     

    (2)  Find the exact length of the perimeter of the minor segment bounded by the chord    and the arc  .   (2 marks)

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  2. (1)  ²
  3. (2)  
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i.   
   
   
 

 

 

 

ii. (1)   
   
   
    ² 

 

ii. (2)   
 
 
 

 

 
 

 

Trigonometry, 2ADV T1 2013 HSC 14c

2013 14c

 
The right-angled triangle    has hypotenuse  . The point    is on    such that  ,   and  .

Using the sine rule, or otherwise, find the exact value of  .   (3 marks)

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♦ Mean mark 36%.
STRATEGY TIP: The hint to use the sine rule should flag to students that they will be dealing in non-right angled trig (i.e. ) and to direct their energies at initially finding and .