Trigonometry in Right-Angled Triangles

Scheme of work: GCSE Higher: Year 10: Term 3: Trigonometry in Right-Angled Triangles

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 x = Opp/Hyp, Cos x = Adj/Hyp, Tan x = 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 and cos for = 0°, 30°, 45°, 0°, and 90°.; know the exact value of Tan 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 the 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 label the sides to identify the correct ratio clearly.
  • 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.

Trigonometry in Right-Angled Triangles Resources

Mr Mathematics Blog

Problem-Solving with Angles in Polygons

How to teach problem solving with angles in polygons through scaffolding.

Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.