Trigonometric Ratios: Finding an Angle

Use the inverse trigonometric ratios (sin^-1, cos^-1, tan^-1) to find a missing angle in a right-angled triangle, given two known sides.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Beta: To determine angles
  • Beta: Exercise 24.03, pg 462
  • Beta: Parallel Skills Exercise 24A, pgs 462 & 463
  • Beta: Application: Exercise 24.04, pgs 464 & 465
  • Dr Austin Maths - Plotting Trigonometric Graphs Practice Grid: PDFQuestions PDF · Answers
  • Dr Austin Maths - Mixed Trigonometry Practice Grid: PDFQuestions PDF · Answers
  • Dr Austin Maths - Multi-Step Trigonometry Practice Grid: PDFQuestions PDF · Answers
  • Dr Austin Maths - Exact Trigonometric Ratios Practice Grid: PDFQuestions PDF · Answers
  • Dr Austin Maths - Trigonometry Revision Practice Grid: PDFQuestions PDF · Answers
  • CorbettMaths on using trigonometry to solve for unknown anglesQuestions PDF · Answers

Terminology

  • Trigonometry
  • Trigonometric ratio
  • Right-angled triangle
  • Hypotenuse
  • Adjacent
  • Opposite
  • SOH CAH TOA
  • Inverse trigonometric function
  • Exact trigonometric ratio
  • Angle of elevation
  • Angle of depression

Task goals

  • Label the hypotenuse, opposite, and adjacent sides of a right-angled triangle relative to an unknown marked angle, in any orientation.
  • Choose the correct ratio (sin, cos, or tan) from the two given sides, using SOH CAH TOA.
  • Find a missing angle by substituting the two known sides into the chosen ratio and applying the inverse trigonometric function.
  • Round an angle answer to a stated accuracy (1 decimal place unless told otherwise) when the result is not exact.
  • Recall exact angle values (0, 30, 45, 60, 90 degrees) from a stated exact trigonometric ratio without a calculator.
  • Apply the skill to real-world contexts, including angles of elevation and depression, and to multi-step problems that chain a side-finding step into an angle-finding step.

Key skills

  • Trigonometry
  • SOHCAHTOA
  • Find angles
  • Inverse trig
  • Exact trig ratios
  • Multi step
  • Right triangles

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  • 3 difficulty levels
  • Answers included
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