Kicking for goal

Kicking for goal

Pencil and paper
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This task is about using trigonometry to find missing lengths.
View from side
kicking-goal-diagram-1.png  
View from top
kicking-goal-diagram-2.png
[Not drawn to scale]
Tiaki is about to kick for goal.
He is kicking from the right-hand side of the goal post from a distance of 33.0 metres, as shown in the diagrams above. 
a)
The distance between the two goal posts is 5.6 metres.
Calculate how far Tiaki is from the left-hand goal post. Show all your working in the box below.
 
 

 

 

 

Tiaki is __________ metres from the left-hand goal post.
 
b)
 
Tiaki aims his kick directly at the right-hand goal post. The wind takes the ball 10° off course to the left.
i) Work out how far the ball passes to the left of the right-hand goal post. Show all your working in the box below.
 
 

 

 

 

The ball passes __________ metres from the left of the right-hand goal post.
 
 
 ii)
Does the ball pass between the goal posts?     Yes   /   No   (Circle one)

Explain your answer.
 

 
 
Task administration: 
This task can be completed with pencil and paper.
Level:
6
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
trigonometry, right angled triangles, pythagoras theorem
Description of task: 
In the context of kicking a goal at rugby, students use Pythagoras' theorem to calculate distance. Students then use trigonometry to work out if the kick passes through the posts.
Answers/responses: 

 

Y11 (09/2001)

a)

  

33.47 [Accept 33.4-33.5]

Evidence of Pythagoras' theorem z = (5.62 + 332) used, but error in calculation.

easy

very easy

b)

i)

 

 

 

 

 

 

 

 

 

 


ii)

 

Any 1 of:

  • 33tan10° = 5.82 m (also accept 5.8)
  • = tanם = 9.63° (also accept 9.6°)
  • sin =
    sin = 0.17 (2 d.p.)
    = 9.63°
  • cos =
    cos = 0.99 (2 d.p.)
    = 9.61°

Puts numbers into tan, sin, or cos function or uses sine rule or cosine rule but one error is made, including:

  • an error in transcribing numbers from diagram
    (or part a))
  • incorrect placement of numbers in trigonometry function or rule.

Yes, and any 1 of:

  • The angle at which the wind takes the ball off course has to be less than 9.6° to get within the goal posts.
  • The distance (5.82 m) calculated is greater than the width (5.6 m) of the goal posts.
    or
  • Accept alternative explanation if consistent with answer given in b)i).

difficult

 

 

 

 

 

 


difficult

 

 

 

difficult

NOTE: This item was trialled with students having access to Pythagoras' theorem and trigonometry ratios.