Sails for the yacht

Sails for the yacht

Pencil and paper
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This task is about using trigonometry to calculate lengths of a triangle.
sails-for-the-yacht-diagram.png
[Not drawn to scale]
 
Maia is drawing a pattern so she can make two sails for her yacht.
She calculates the lengths of sides x and y using the measurements above and trigonometry.
 
a)
Calculate the length of side x. Use the space provided to show your working.
 
 
 
 
 
 
Length of side x = __________ metres.
 
b) i)
Use trigonometry to show two different ways Maia could find the length of side y.
Use the numbers in the diagram above.
  
1:
 
 
 
 
 
 
 
 2:
 
 
ii) 
 
Use one of your methods to calculate the length of side y. 
 
 
 
 
 
 
Length of side y = ________ metres. 
Task administration: 
This task can be completed with pencil and paper.
Level:
6
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
trigonometry, sine, cosine, tangents
Description of task: 
Students use their knowledge of the trigonometric functions sine, cosine, and tangent to calculate the length of sides of sails in a diagram of a yacht.
Answers/responses: 

 

Y11 (10/2001)

a)

  

4.56 [Accept answers within the range 4.5-4.6].
NOTE: Full marks given even if working not shown.
Tan function (x = 17tan15), sine rule, or other possible method of solution (e.g., Pythagoras' theorem using trigonometry) identified but an error in calculation made.

moderate

easy

b)

i)

 

 

 

 

ii)

Any 2 of:

  • 17 ÷ sin65°
  • 17 ÷ cos25°
  • Other possible methods of solution, e.g.,

Pythagoras' theorem using trigonometry.
NOTE: Do not accept trig ratios or sine rule without appropriate numbers included.
18.76 [Accept answers within the range 18.7 to 18.8].


2 correct – very difficult

1 correct – difficult


difficult

NOTE: This test has been trialled with students having access to a formula sheet with Pythagoras' theorem and trigonometry functions on it.