Applications of Trigonometric Ratios: Finding Angles

Model a real-world situation with a right-angled triangle, choose the appropriate inverse trigonometric ratio, and calculate an unknown angle of elevation, depression, inclination, or slope.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • GM5-10
New NZC (2026)
  • NZC26-P4-GEO-SHP-P-Y10-01

Resources

  • CorbettMaths on using trigonometry to solve for unknown anglesQuestions PDF · Answers
  • Beta: Exercise 24.03, pg 462
  • Beta: Parallel Skills Exercise 24A, pgs 462 & 463
  • Beta: Application: Exercise 24.04, pgs 464 & 465

Terminology

  • inverse trigonometry functions
  • SOH CAH TOA

Task goals

  • Label the hypotenuse, adjacent, and opposite sides of a right-angled triangle relative to an unknown angle.
  • Find a missing angle of a right-angled triangle given two known side lengths, using the correct inverse trigonometric function (sin^-1, cos^-1, or tan^-1).
  • Find a missing angle from a labelled diagram giving two side lengths of a right-angled triangle.
  • Round a calculated angle to one decimal place or the nearest degree, as instructed.
  • Solve a real-world worded problem (such as a ladder, ramp, roof, kite, or wire) by finding the angle a right-angled triangle makes with the ground or horizontal.
  • Explain why the inverse trigonometric function is needed to find an angle, rather than reporting the trig ratio itself as the angle.
  • Solve a multi-step or two-way real-world problem that combines finding an angle with finding a related length, or that requires comparing a calculated angle against a stated threshold.

Where this fits

What leads into this objective, and where it goes next.

Before

Interior angles of a triangle

Interior angles of a triangle

Regular/irregular polygon

Regular/irregular polygon

Internal and external

Internal and external

You are here

Applications of Trigonometric Ratios: Finding Angles

Applications of Trigonometric Ratios: Finding Angles

Do

Using the properties of similarity in 2D shapes, including right-angled triangles, to find unknown lengths and angles

Statement▸
Year 10 · Geometry · Shapes
NZC26-P4-GEO-SHP-P-Y10-01

Next

Year 10 is the last year of this phase — the curriculum lists nothing after this. Extension resources: Trigonometric Ratios: Finding a Side, Using the Sine Rule to find missing sides.

Also under GM5-10:

Explore the whole sequence →

For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.