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Edexcel GCSE Maths

Angles, Pythagoras and trigonometry — Edexcel GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 5 minutes to read.

Angle rules

  • Angles on a straight line add to 180°, around a point 360°.
  • Angles in a triangle add to 180°, in a quadrilateral 360°.
  • Exterior angle of a polygon = 360 ÷ number of sides.

Right-angled triangles

  • Pythagoras: a² + b² = c², where c is the hypotenuse.
  • SOHCAHTOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
  • Use the inverse function (sin⁻¹ etc.) when finding an angle.

Key terms

Hypotenuse
The longest side of a right-angled triangle, opposite the right angle.
Interior angle
An angle inside a polygon at a vertex.
Bearing
An angle measured clockwise from north, written with three figures.
Sine rule
A rule linking sides and angles in any triangle, used when SOHCAHTOA doesn't apply.
Cosine rule
A rule for finding a side or angle in a non-right-angled triangle.
Slant height
The distance from the base edge to the apex along the surface of a cone.

Common exam traps

  • Using Pythagoras on a triangle that isn't right-angled.
  • Forgetting to use the inverse trig function when finding an angle.
  • Writing bearings with fewer than three figures (e.g. 45° instead of 045°).

Practice questions with answers

  1. 1. A right-angled triangle has legs 6 cm and 8 cm. Find the hypotenuse.

    Answer: 10 cm

    6² + 8² = 100, √100 = 10.

  2. 2. Which ratio uses the opposite and adjacent sides?

    • • sin
    • • cos
    • • tan
    • • Pythagoras

    Answer: tan

    TOA: tan = opposite ÷ adjacent.

  3. 3. Find the exterior angle of a regular hexagon.

    Answer: 60°

    360 ÷ 6 = 60.

  4. 4. Two angles on a straight line: one is 118°. Find the other.

    Answer: 62°

    180 − 118 = 62.

  5. 5. Find the area of a circle with radius 5 cm. Use π = 3.14.

    Answer: 78.5 cm²

    Area = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 cm².

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