ReviseRush logoREVISERUSH

AQA GCSE Maths

Trigonometry: right-angled and non-right-angled triangles — AQA GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 7 minutes to read.

Right-angled triangle trig

  • SOHCAHTOA: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent.
  • Pythagoras' theorem: a^2 + b^2 = c^2, where c is the hypotenuse.
  • Use inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to find missing angles.

Non-right-angled triangles

  • Sine rule: a/sin(A) = b/sin(B) = c/sin(C), used when you know an angle-side opposite pair.
  • Cosine rule for a side: a^2 = b^2 + c^2 - 2bc·cos(A).
  • Cosine rule for an angle: cos(A) = (b^2 + c^2 - a^2) ÷ (2bc).

Key terms

Hypotenuse
The longest side of a right-angled triangle, opposite the right angle.
Opposite
The side opposite the angle being used in a right-angled triangle.
Adjacent
The side next to the angle being used (not the hypotenuse).
Sine rule
a/sin(A) = b/sin(B) = c/sin(C), relating sides and opposite angles.
Cosine rule
A rule linking all three sides and one angle of any triangle.
Angle of elevation
The angle upward from the horizontal to an object.

Common exam traps

  • Mixing up opposite and adjacent sides relative to the marked angle.
  • Using the sine rule when the cosine rule is needed (no angle-side opposite pair).
  • Forgetting to take the square root at the end of Pythagoras' theorem.

Practice questions with answers

  1. 1. A right triangle has opposite = 6, hypotenuse = 10. Find sin(θ).

    Answer: 0.6

    sin(θ) = opposite/hypotenuse = 6/10 = 0.6.

  2. 2. Find the hypotenuse of a right triangle with legs 3 and 4.

    Answer: 5

    Pythagoras: 3^2+4^2=9+16=25, sqrt(25)=5.

  3. 3. In SOHCAHTOA, which ratio uses opposite and adjacent?

    • • sin
    • • cos
    • • tan
    • • none

    Answer: tan

    tan(θ) = opposite/adjacent (TOA).

  4. 4. A ladder leans against a wall, adjacent = 5, angle = 60°. Find the height (opposite) to 1 dp.

    Answer: 8.7

    tan(60°) = opposite/5, opposite = 5 × tan(60°) ≈ 5 × 1.732 = 8.66 ≈ 8.7.

  5. 5. Use the sine rule: a=8, A=40°, B=60°. Find side b to 1 dp.

    Answer: 10.8

    b = a×sin(B)/sin(A) = 8×sin(60)/sin(40) = 8×0.866/0.643 ≈ 10.8.

Keep going in the app

This topic has 51 questions in total, plus flashcards, cram mode and Grade 9 Push challenges.

Open the full topic Quick-fire quiz

More free Maths revision

ReviseRush is an independent educational revision aid. It is not affiliated with, endorsed by or connected to AQA, Edexcel, OCR, WJEC, Pearson or any exam board. All notes and questions are original. Always check content against your official course and specification. No grade outcome is guaranteed.