# 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 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 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.