Planning tool

Students:

• use the correct trigonometrical ratio to solve problems involving the length of sides
• apply knowledge of scale factor and similar figures to solve simple problems
• apply knowledge of trigonometry to solve simple problems
• communicate their thinking, reasoning and solutions.

Some students may:

• assume a diagram is to scale and make assumptions based on this.
• believe that corresponding sides are ‘matching’ regardless of the orientation of the shape. In identifying corresponding sides, it is helpful to ensure the orientation of the shapes is the same, making the corresponding sides easier to identify. The use of concrete materials and dynamic geometry software can assist students to visualise shapes and objects in different orientations. Support students to consider each entire shape when deciding if they are similar.
• not check the scale factor is the same for every side.
• not recognise that a triangle is a right triangle.
• try to use Pythagoras’ theorem with non-right triangles.
• misidentify the trigonometrical ratios to be used.
• apply trigonometrical ratios to non-right triangles.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning about the three trigonometrical ratios.
• We are learning to use the trigonometrical ratios to solve a problem involving the side lengths and angles in a right-angle triangle.

Why are we learning about this?

Trigonometry is the basis of much higher-level mathematics. It is used in many professional areas such as architecture, engineering, aviation, satellite technology and cartography.

What to do

History of trigonometry

• Write down your responses to these questions:
  • Where did the idea of trigonometry come from?
  • How did it develop?
  • Which civilisations were involved?
• The following resource has three articles. View The history of trigonometry: Part 1. Next, view the other two articles: Part 2 and Part 3.
• Write a summary of what you found out with at least three key developments that interested you. Include ways a right-angled triangle was used to measure heights and distances.

Success criteria

• I can identify and label the sides of a right-angled triangle according to a reference angle (θ – hyp, adj, opp).
• I can state the three trigonometrical ratios.
• I can use the trigonometrical ratios to solve a problem involving the side lengths and angles in a right-angled triangle.