Trigonometry in Right-Angled Triangles

Students are guided to discover the Sine, Cosine and Tangent ratios of right-angled triangles.  As learning progresses they learn how to calculate a missing angle and length in right-angled triangles and solve problems involving 3D shapes.

This topic takes place in Year 10 Term 3 and follows on from Pythagoras’ Theorem.


Trigonometry in Right-Angled Triangles Lessons
Revision Lessons

Prerequisite Knowledge

  • Express a multiplicative relationship between two quantities
  • Understand and use proportion as equality of ratios
  • Know the formulae for: Pythagoras’ theorem, a2 + b2 = c2
  • Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the
  • Base angles of an isosceles triangle are equal, and use known results to obtain simple proofs

Success Criteria

  • Know the trigonometric ratios, Sin ϑ = Opp/Hyp, Cos ϑ = Adj/Hyp, Tan ϑ = Opp/Adj
  • Apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures
  • Know the exact values of Sin ϑ and Cos Sin ϑ for ϑ = 0°, 30°, 45°, 60°, and 90°.; know the exact value of Tan ϑ for 0°, 30°, 45° and 60°.

Key Concepts

  • Sin, Cos and Tan are trigonometric functions that are used to find lengths and angles in right-angled triangles.
  • The ‘hypotenuse’ is opposite the right angle, the ‘opposite’ refers to the side that is opposite the angle in question and ‘adjacent’ side runs adjacent to the angle.
  • The inverse operations of sin, cos and tan are pronounced arcos, arcsin and arctan.
  • Students need to be confident using diagram notation to draw 2D diagrams from problems in 3D.

Common Misconceptions

  • Students often have difficulty knowing which trigonometric ratio to apply. Encourage them to clearly label the sides to identify the correct ratio.
  • Use SOHCAHTOA as a memory aid as students often forget the trigonometric ratios.
  • When using trigonometric ratios to calculate angles students often forget to use the inverse functions.
  • Students often try to apply right-angled formulae to non-right-angled triangles.

Mr Mathematics Blog

Trigonometric Identities Sin, Cos and Tan

How to introduce the sin, cos and tan trigonometric identities.

Calculating a Reverse Percentage

How to teach calculating the original amount after a percentage change.

Comparing Datasets using the Mean and Range

The importance of the range when comparing comparing datasets.