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Why do this problem?

There are several different ways of solving this problem. It is a good example to bring home the point that, to be an expert problem solver, and to understand a piece of mathematics, it is not enough to find an answer. One should ask oneself "Have I used the best method?". This problem can be solved using trig formulae and the cosine rule but it can be solved more straightforwardly using only Pythagoras theorem.

Possible approach

Challenge the class to find different methods of solution.

Key question

How do we interpret the two solutions?

Is the diagram correct for both solutions?


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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