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Trigonometry: measuring with triangles
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Full details
TLF ID:
L2326
Year level:
7–9
Series description:
Students explore how the angles and side-length properties of similar right-angled triangles may be applied in measurement situations to calculate unknown side lengths and angles.
Learning object description:
Students see how the early Greeks and Egyptians used the properties of similar right-angled triangles to solve measurement problems. They then use equivalent ratios to calculate the lengths of a triangle's sides: the height of an object or the length of a shadow. This task is repeated twice more with increasingly complex ratios. The next demonstration focuses on the properties of similar isosceles right-angled triangles. Students then use ratio in three pairs of similar isosceles right-angled triangles to find the unknown value on one triangle.
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:
The learning object:
- 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.
Learning area:
Mathematics
Keywords:
Corresponding angles, Corresponding sides, Equivalence, Length, Proportions, Ratios, Right angled triangles, Shadows, Sides, Similarity, Trigonometry
Rights:
© Curriculum Corporation, 2005