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Right angled trigonometry

Right angled trigonometry for Functional Skills Design and Technology: what it means, how to set the working out, and the questions it is asked in.
  • Functional Skills
  • Design and Technology
  • Spec S20 · S13 · S11
  • 14 min read
  • 8 revision boxes

Introduction

2 boxes
1 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.
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.
5 rows

The right angled trigonometry reference table

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: x2+5x+6=0x^2 + 5x + 6 = 0.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 2 column 1
Row 2 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 3 column 1
Row 3 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 4 column 1
Row 4 column 2
x2+5x+6=0x^2 + 5x + 6 = 0

Learning

4 boxes
5 steps

How to work with right angled trigonometry

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
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: ≈160\approx 160.
Answer: 49=7\sqrt{49} = 7
3 rules

Key facts: Right angled trigonometry

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

  • 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.
    49=7\sqrt{49} = 7

  • Rule 3

    How right angled trigonometry behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
3 steps

How to work with right angled trigonometry

The examiner marks the working, so a correct answer with no method still drops marks.
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.
  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: ≈160\approx 160.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Right angled trigonometry

This idea appears again in the higher-mark questions, so it is worth over-learning.

  • Rule 1

    How right angled trigonometry behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

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

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Examples

2 boxes
4 marks · worked

Worked example: right angled trigonometry

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
4 marks · worked

Practice question 8: 34×25\frac{3}{4} \times \frac{2}{5}

Work through the method one line at a time and write down what changes at each step.

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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 Functional Skills Design and Technology paper?
Yes — it sits in the Writing and structure strand.