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.

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