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The Sine Ratio Overview
Fire-fighters using ladders in emergency situations, a young water-skier preparing for a competition, and a champion Paralympic athlete show how important the relationships between sides and angles in right-angled triangles are within each of their disciplines. The programme concentrates on the sine ratio and its applications. It shows how appropriate triangles and dimensions can be drawn from real-life situations. Clear views of the real objects, along with helpful graphics and careful explanations, demonstrate how the necessary information is selected and used. We see how to: - draw an appropriate right-angled triangle
- identify and name sides in relation to the angle being worked with
- substitute values in the formula ‘sin = opposite / hypotenuse’
- calculate the length of a side opposite to a known angle in a right-angled triangle
- calculate the length of the hypotenuse
- select appropriate calculator functions
- substitute lengths of sides into the formula in order to calculate an angle
Although the programme deals only with the sine ratio, it would still be relevant to students who have been introduced to all three ratios. Similar triangles and the constant ratios that they produce are mentioned. It is assumed that students will have done a fair amount of preparatory work within the topic prior to viewing. The programme would be most useful as a means of showing students how the theory relates to the real world. It could be used to build and consolidate understanding of the topic alongside other work. It could also be helpful in reinforcing, or revising, the techniques needed to solve the types of problem relating to the topic that are most often encountered. The content is linked to the requirements of GCSE Intermediate Mathematics. It includes tips for answering exam questions, and a discussion of a typical exam error (‘Tick or Trash’). The lively contexts should prove interesting to students at this level and help them to appreciate the applications of this important branch of mathematics.
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