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Learning objects Trigonometry: measuring with triangles

TLF ID L2326

Compare the shadows cast by a small stick and a larger object such as a column of a Greek building. Check the angles at which the shadows are cast and confirm whether the two objects create similar triangles. Use equivalent ratios to calculate the lengths of a triangle's sides: the height of an object or the length of a shadow. Explore how right-angled triangles can be used in measurement, including special properties of the isosceles right-angled triangle. 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 for indirect measurement of tall objects.
  • 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
  • Highlights early applications of trigonometry by ancient Greeks and Egyptians.
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;
    • Experiment;
    • 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 3130 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:
    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.