The tangent ratio

Objective. Connect an angle to opposite and adjacent sides.

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2. Worked example
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Learn: the key idea

The tangent ratio develops a connected mathematical idea rather than an isolated trick. Solve right-triangle problems with exact geometric relationships. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Which ratio is tangent?

1 $Identify the known information, the unknown and any conditions.$
2 $Choose a diagram, table, graph or algebraic representation that exposes the structure.$
3 $Apply the relevant rule one justified step at a time, keeping exact values where useful.$
4 $Check by substitution, inverse reasoning or estimation. The result is opposite/adjacent.$

Answer: opposite/adjacent

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Practice

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Common mistake. A common error in the tangent ratio is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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