Trigonometric Ratios: Finding a Side

Use the trigonometric ratios (SOH CAH TOA) to find a missing side in a right-angled triangle, given one angle and one other side.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Beta: To determine sides
  • Beta: Exercise 22.01, pg 422
  • Beta: Exercise 22.13, pg 441
  • Beta: Exercise 22.14, pg 442
  • Beta: Parallel Skills Exercise 22C, pgs 442 & 443
  • Beta: Application: Ex 23.03, pgs 448 & 449
  • Dr Austin Maths - Plotting Trigonometric Graphs Practice Grid: PDFQuestions PDF · Answers
  • Dr Austin Maths - Mixed Trigonometry Practice Grid: PDFQuestions PDF · Answers
  • CorbettMaths on using trigonometry to solve for unknown sidesQuestions PDF · Answers

Terminology

  • Trigonometry
  • Trigonometric ratio
  • Right-angled triangle
  • Hypotenuse
  • Adjacent
  • Opposite
  • SOH CAH TOA
  • Sine
  • Cosine
  • Tangent
  • Angle of elevation
  • Angle of depression

Task goals

  • Label the hypotenuse, opposite, and adjacent sides of a right-angled triangle relative to a marked angle, in any orientation.
  • Choose the correct ratio (sin, cos, or tan) from the marked angle and the pair of sides involved, using SOH CAH TOA.
  • Find a missing opposite, adjacent, or hypotenuse side by substituting into the chosen ratio and solving.
  • Round an answer to a stated accuracy (3 significant figures or a given number of decimal places) when the result is not exact.
  • Apply the ratios to real-world contexts, including angles of elevation and depression.

Key skills

  • Trigonometry
  • SOHCAHTOA
  • Find sides
  • Find angles
  • Inverse trig
  • Right triangles

Quick stats

  • 0 total questions
  • 3 difficulty levels
  • Answers included
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