Trigonometry – Problems with Right-Angled Triangles

Introducing Trigonometry with Right-Angled Triangles

Angles in a Right-Angled Triangle

Lengths in a Right-Angled Triangle

Problems with 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 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 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.

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.