Learning objects Trigonometry: using cosine

TLF ID L2333

Solve measurement problems involving right-angled triangles by using similar triangles and trigonometric methods, including cosine values. Identify corresponding sides and ratio relationships in similar triangles. Solve measurement problems by using cosine values to calculate side lengths in triangles. For example, find the width of a moat, given one angle and distance to the top of a castle. This learning object is one in a series of ten objects.

Educational details

Key learning objectives
  • Students apply knowledge of relationships between sides of similar triangles to calculate side lengths in right-angled triangles.
  • Students use multiplicative and ratio strategies to solve measurement problems.
Educational value
  • Introduces trigonometric techniques to solve problems involving indirect measurement of lengths and heights.
  • Models definitions of the trigonometric ratios using a unit circle.
  • Helps students to identify corresponding sides of similar triangles.
  • Models measurement situations involving equivalent ratios.
  • Provides a range of equations including an unknown variable that can be solved by using multiplicative facts and strategies.
Year level

9; 10

Learning area
  • mathematics
  • Mathematics/Measurement and geometry
    • Mathematics/Angles
    • Mathematics/Similarity
    • Mathematics/Ratio and proportion
    • Mathematics/Triangles
    • Analysis;
    • Application;
    • Comprehension;
    • Knowledge
    Student activity
    • Interactives;
    • Analysis;
    • Modelling
    Learning design
    • Experiential learning;
    • Independent learning;
    • Problem solving;
    • Visual learning

    Other details

    • Technical implementer
    • Script writer
    • Name: Rod Rees
    • Organisation: Rees Films Pty Ltd
    • Address: Blackburn VIC 3105 Australia
    • Subject matter expert
    • Name: Howard Reeves
    • Address: Lindisfarne TAS 7015 Australia
    • Publisher
    • Date of contribution: 20 Sep 2013
    • Organisation: Education Services Australia
    • Address: Melbourne VIC 3000 Australia
    • URL: http://www.esa.edu.au/
    Access profile
    • Colour independence
    • Hearing independence
    Learning resource type
    • Interactive Resource
    • Microsoft Internet Explorer - minimum version: 8.0 (MS-Windows) - maximum version: 9.0 (MS-Windows)
    • Firefox - minimum version: (MS-Windows)
    • Safari - minimum version: 5.1 (MacOS)
    Operating systems
    • MacOS - minimum version: 10.6
    • MS-Windows - minimum version: XP - maximum version: 7
    • © Education Services Australia Ltd, 2013, except where indicated under Acknowledgements.