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.
Teacher notes
- There is a progression from the informal ratio techniques used in ancient cultures to the more formal methods of right-angled triangle trigonometry.
- A step-by-step approach with scaffolding and informative feedback leads students through establishing similarity, identifying corresponding sides, establishing equivalent ratios and finding unknown lengths.
- Introduces students to the formal trigonometric ratios sine, cosine and tangent and their use in triangle measurement contexts.
- Demonstrates and maintains the fundamental underpinning links between similarity and triangle trigonometry.
Learning objects
| Trigonometry: measuring with triangles Students see how the early Greeks and Egyptians used the properties of similar right-angle triangles to solve measurement problems. They then identify and record the relevant ratios in two similar right-angle triangles to find the unknown height of one of them (represented as the height of a column). Students then use ratio in three pairs of similar isosceles right-angle triangles to find the unknown value on one triangle. |
| Trigonometry: similar triangles Students manipulate and identify the properties of similar right-angle triangles. |
| Trigonometry: sine Students use a 'unit circle' tool to complete a table of values concerning sine. |
| Trigonometry: cosine Students use a 'unit circle' tool to complete a table of values concerning cosine. |
| Trigonometry: tangent Students use a 'unit circle' tool to complete a table of values concerning tan. |
| Trigonometry: using sine Students use sine and the properties of the right-angle triangles to solve measurement problems. |
| Trigonometry: using cosine Students use cosine and the properties of the right-angle triangles to solve measurement problems. |
| Trigonometry: using tan Students use tan and the properties of the right-angle triangles to solve measurement problems. |
| Trigonometry: finding the hypotenuse Students use sine to find the hypotenuse. |
| Trigonometry: finding the angles Students use tri ratios to find missing angles. |