3.7 Pythagoras' theorem and trigonometry
Solve two- and three-dimensional length and angle problems with Pythagoras and trigonometric relationships.
How to study WJEC GCSE Mathematics and Numeracy
Move from concept and notation to a justified method, show a complete mathematical chain, check scale and units, and interpret the answer in context.
Core concepts
Concept 1
Use Pythagoras' theorem and its converse in two and three dimensions.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Use right-triangle trigonometry and extend to non-right triangles at Higher tier.
Exam cue: Identify the triangle, label known and required sides or angles, then justify the theorem or ratio chosen.
Concept 3
Use trigonometric graphs, exact values and supplied sine, cosine and area rules where specified.
Exam cue: Show a complete mathematical chain, use correct notation and units, and interpret or check the result in its original context.
Concept 4
Current matrix coverage: Unit 3. Read the exact subpoint scope in each applicable unit column.
Concept 5
Foundation content is shown in standard type in the specification; bold additions apply only to Higher Tier.
Risk pitfalls and guardrails
Applying right-triangle trigonometry to a non-right triangle or leaving the calculator in the wrong angular mode.
Guardrail: The Unit 1 and Unit 3 lists are limited and Unit 2 supplies none; preserve exact values and know all other required relationships.
Assuming that every subpoint in a cross-unit strand appears in all three papers, rather than reading the correct matrix column.
Guardrail: Read the precise subpoint in the applicable unit column; a cross-unit strand does not mean every subpoint appears in every paper.
Using a Higher-only method or expectation for a Foundation entry, or importing the outgoing Mathematics/Mathematics-Numeracy structure.
Guardrail: Standard type applies to Foundation and Higher; bold specification additions are Higher-only. There is no Intermediate Tier.
Memory anchors
Pythagoras
In a right triangle, the hypotenuse squared equals the sum of the other side squares.
Sine ratio
In a right triangle, sine equals opposite divided by hypotenuse.
Cosine ratio
In a right triangle, cosine equals adjacent divided by hypotenuse.
Tangent ratio
In a right triangle, tangent equals opposite divided by adjacent.
Non-right triangle
Higher-tier sine and cosine rules extend trigonometry beyond right triangles.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
A right triangle has legs 9 cm and 12 cm. Find its hypotenuse.
A right-angled frame's longest bar is 13 cm and one perpendicular bar is 5 cm. Calculate the remaining bar.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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