Which Rule?

'Master the art of working out when best to apply which rule to trigonometry problems'

From SOHCAHTOA to cosine rule to Pythagoras's theorem, it can be difficult to know which is the most appropriate rule to apply in given situations. Sure, when doing an exercise on the cosine rule, you know what to look for, but questions don't often tell you which rule you are expected to use. This is all part of the art of efficient problem solving and to do it, one has to be good at speculating quickly and not be afraid to go down a couple of wrong paths before finding a helpful one. This activity isn't about the calculating of answers to questions, but about plotting a path through problems and spotting the features that help direct us.

You have to speculate to accumulate!

Below is a prezi slideshow that talks you through the main aims of this task! (click to move through the stages of the prezi)


  • To practise the application of SOHCAHTOA, sine rule, cosine rule and Pythagoras's theorem to different situations and problems.
  • To practise speculating as a problem solving technique
  • To practise identifying the most helpful routes through problems with trigonometry


The  Which Rule worksheet is a paper based activity that consists of a series of 'fill in the blanks' tasks. Some reasoning behind the activity is discussed in the Which rule teacher's Notes.

Example Task

Below is a screen shot of one of the tasks to give a quick flavour of what its all about.

Syllabus links

This is relevant both right-angled trigonometry and non right-angled trigonometry from the studies syllabus. It follows on well from work on understanding and applying the various rules for trigonometry.

New - Sections 5.2 and 5.3, Previous, Sections 5.3 and 5.4


  • Labelled triangles and partially completed expressions are given and students are asked to use their knowledge of trig rules to fill in the blanks.
  • Students are then asked to identify which of the expressions would be the most useful to solve for given variables.
  • A labelled triangle is given along with some associated expressions. Students are asked to identify which of the expressions are correct and which are false.
  • For some given problems, students are asked a series of multiple choice questions about their options for approaching the problems.
  • Students are given some problems and asked to make bullet point lists of which rule they would use to solve for which variable and then compare their strategies with each other.
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