The Tangent Ratio

Teachers' Notes

The programme aims to support students' ability to visualise real-life situations in an abstract way by bringing the two together on screen. The examples were chosen to reflect contexts familiar to students from texts and exams. Each type of trigonometric calculation (finding an angle, finding the opposite and finding the adjacent) is demonstrated in detail with the necessary rearrangements of the basic formula 'Tan A = opposite/adjacent' discussed. Some preparatory work on similar triangles and constant ratios would be helpful prior to viewing. Students will probably need considerable classroom reinforcement of the techniques covered, particularly if the programme is shown at the start of the topic. Students may benefit from viewing short sections of the programme as they progress through stages of the work and then view the entire programme to summarise the main points. Calculator usage is covered, but students could work through the given examples to establish keystrokes for their own calculator either during or after viewing.

Knowledge of the other ratios is not assumed. Therefore, the programme could be viewed by students who have only met the tangent or used to provide enrichment and context alongside teaching of all three ratios. It could be used in conjunction with 'The 'Sine Ratio' programme from series 1 of Maths 4 Real, and both programmes would be suitable as revision or consolidation tools.

The answers to Worksheet 1 could be used as the basis for a discussion after viewing. For revision purposes, students may find it useful to have their own copy of the Key Facts and Exam Tips section of these notes. These could be edited and amended to meet individual needs.

The roller coaster item used opposite = 30 or 20 and adjacent = 33 or 22 to find the angle of 42º.

The height (20m) of the Angel of the North was calculated from a distance of 23.8m with an angle of elevation to the top of the head of 40º.

At the lighthouse Katie was 41.6m above sea level and she viewed Jamie at an angle of depression of 10º, making his distance from the rocks 236m.