# Trigonometry

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 trianglesStudents 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 trianglesStudents manipulate and identify the properties of similar right-angle triangles. Trigonometry: sineStudents use a 'unit circle' tool to complete a table of values concerning sine. Trigonometry: cosineStudents use a 'unit circle' tool to complete a table of values concerning cosine. Trigonometry: tangentStudents use a 'unit circle' tool to complete a table of values concerning tan. Trigonometry: using sineStudents use sine and the properties of the right-angle triangles to solve measurement problems. Trigonometry: using cosineStudents use cosine and the properties of the right-angle triangles to solve measurement problems. Trigonometry: using tanStudents use tan and the properties of the right-angle triangles to solve measurement problems. Trigonometry: finding the hypotenuseStudents use sine to find the hypotenuse. Trigonometry: finding the anglesStudents use tri ratios to find missing angles.