# 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.

##### 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.

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