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Right angled trigonometry

Right angled trigonometry for GCSE Sociology AQA: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Sociology
  • Spec G13 · G11 · G16
  • 14 min read
  • 9 revision boxes

Introduction

2 boxes
2 min read

What is right angled trigonometry?

Listen to this box

Transcript

A short spoken summary of right angled trigonometry and where it is used.

A spoken walk-through of right angled trigonometry before you read the notes.
This idea appears again in the higher-mark questions, so it is worth over-learning.
2 rows

The right angled trigonometry reference table

The examiner marks the working, so a correct answer with no method still drops marks.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 1
Row 3 column 2
≈160\approx 160
Row 4 column 1
Row 4 column 2
34×25\frac{3}{4} \times \frac{2}{5}

Learning

5 boxes
3 steps

How to work with right angled trigonometry

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing right angled trigonometry laid out step by step

The same idea drawn out, so the method is visible.
  1. Read the question and write down what is being asked for.
  2. Set out the working for right angled trigonometry in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Right angled trigonometry

Sketch the shape even when the question does not ask for one — it makes the next step obvious.

  • Rule 1

    How right angled trigonometry behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How right angled trigonometry behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
5 steps

How to work with right angled trigonometry

This idea appears again in the higher-mark questions, so it is worth over-learning.
The layout below is the one the mark scheme expects.

Diagram showing right angled trigonometry laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ≈160\approx 160.
  1. Read the question and write down what is being asked for.
  2. Set out the working for right angled trigonometry in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Right angled trigonometry

The examiner marks the working, so a correct answer with no method still drops marks.
The layout below is the one the mark scheme expects.

Diagram showing right angled trigonometry laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ×10\times 10 moves every digit one column left.

  • Rule 1

    How right angled trigonometry behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How right angled trigonometry behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 3

    How right angled trigonometry behaves in the 3rd of the cases the specification names.
    ≈160\approx 160
4 steps

How to work with right angled trigonometry

Practise the routine version until it is automatic, then move to the multi-step questions.
  1. Read the question and write down what is being asked for.
  2. Set out the working for right angled trigonometry in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: ≈160\approx 160

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Examples

2 boxes
3 marks · worked

Worked example: right angled trigonometry

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: 49=7\sqrt{49} = 7.
2 marks · worked

Practice question 9: ≈160\approx 160

Read the units in the question before you start; a converted unit is the most common slip.

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Common questions

How many marks is right angled trigonometry usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Sociology AQA paper?
Yes — it sits in the Writing and structure strand.