Planning tool

Students will:

• identify the opposite and adjacent sides of a right-angled triangle for a given angle
• state the three trigonometrical ratios
• use the correct trigonometrical ratio to solve a problem involving the side lengths and angles in a right-angle triangle
• use appropriate terminology, diagrams and symbols in mathematical contexts
• select and use the appropriate strategy to solve problems
• provide reasoning to support conclusions that are appropriate to the context
• identify the angle of elevation or depression.

Some students may:

• not appreciate the nature of sine, cosine and tangent – these are ratios, not numbers.
• misidentify the sides of the triangle in relation to the angle given.
• not use the correct trigonometrical ratio and try to apply to non-right-angled 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 how to write a formal proof of a geometric property using the correct mathematical language and notation.
• We are learning how to apply geometrical properties to solve geometry problems.

Why are we learning about this?

• There are many areas where knowledge of shapes and angles is useful.
• It is important that you can communicate your ideas using the correct mathematical terminology and notation.
• If you are going on to study mathematics at a higher level, knowledge of formal proof is important.

What to do

1. Angles of elevation and depression
   This GeoGebra exercise demonstrates the meaning of ‘angle of elevation’ and ‘angle of depression’.
2. The spider and the fly
   A spider is sitting in the middle of one of the smallest walls in my living room and a fly is resting by the side of the window on the opposite wall, 1.5 m above the ground and 0.5 m from the adjacent wall. The room is 5 m long, 4 m wide and 2.5 m high. What is the shortest distance the spider would have to crawl to catch the fly?

   To solve this problem, draw a picture (diagram) of the room, labelling the dimensions. What pathways can the spider take?

3. How high is the mountain?

   Finding the height of an object like a mountain is not as easy as it sounds. The great Adirondack surveyor explains how Verplank Colvin solved this problem in the 1870s using Pythagoras and trigonometry. The methods he devised are still used in surveying today.

Success criteria

• I can identify the opposite and adjacent sides of a right-angled triangle for a given angle.
• I can state the three trigonometrical ratios.
• I can use the correct trigonometrical ratio to solve a problem involving the side lengths and angles in a right-angled triangle.
• I can use appropriate terminology, diagrams and symbols in mathematical contexts.
• I can select and use the appropriate strategy to solve problems.
• I can provide reasoning to support conclusions that are appropriate to the context.
• I can identify the angle of elevation or depression.