# Trigonometry – Problems with Right-Angled Triangles

Scheme of work: GCSE Foundation: Year 11: Term 2: Trigonometry – 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: Pythagorasâ€™ theorem, a2 + b2 = c2
• apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagorasâ€™ 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 dimensional figures.
• know the exact values of Sin x and Cos Sin x for x = 0°, 30°, 45°, 60°, and 90°; know the exact value of Tan x for 0°, 30°, 45° and 60°.

#### Key Concepts

• Sin, Cos and Tan are trigonometric functions that find lengths and angles in right-angled triangles.
• The hypotenuse is opposite the right angle; the opposite refers to the side 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.

#### 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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