Right-angled trigonometry (SOHCAHTOA)

AQA GCSE Maths

8 ready-made resources for teaching Right-angled trigonometry (SOHCAHTOA), written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

Label the sides of a right-angled triangle (opposite, adjacent, hypotenuse) relative to a given angle.
Use the sine, cosine, and tangent ratios to find a missing side length.
Use the sine, cosine, and tangent ratios to find a missing angle.
Solve simple contextual problems (angles of elevation/depression).
Recall and use exact trigonometric values for standard angles (0°, 30°, 45°, 60°, 90°) without a calculator.

Higher tier, in addition

Use the sine rule and cosine rule to solve problems involving non-right-angled triangles.
Calculate the area of a triangle using ½ab sin(C).
Solve multi-step problems combining trigonometry with Pythagoras' theorem or with bearings.

Where students go wrong

Mislabelling opposite and adjacent sides: these are defined relative to the marked angle, not fixed by the triangle's physical orientation.
Selecting the wrong ratio (sine, cosine, or tangent) for the sides given in the question.
Calculator left in the wrong angle mode (degrees vs radians), producing plausible-looking but incorrect answers.
Forgetting to use the inverse trig function when solving for an angle rather than a side.
In non-right-angled triangle problems (Higher), defaulting to SOHCAHTOA instead of recognising that the sine or cosine rule is needed.

How it gets asked in the exam

"Calculate the size of angle x", "Find the length of side y", "The angle of elevation is...", "Work out the area of the triangle".

Key vocabulary

Opposite, adjacent, hypotenuse, sine, cosine, tangent, angle of elevation, angle of depression, sine rule, cosine rule (Higher), included angle.

Assumed prior knowledge

Pythagoras' theorem.
Rearranging equations.
Calculator fluency with trigonometric and inverse trigonometric functions.
Basic angle facts.

How Speca scaffolds this topic

A consistent triangle-labelling routine, mark the angle first, then opposite/adjacent/hypotenuse in the same three colours every time, is one of the highest-leverage scaffolds for this topic.
Provide a simple decision aid ("which two sides or angle do I already know, and which do I want to find?") as a chunked first step before any calculation.
Include an explicit calculator-mode check as a standing step in every worked example, since incorrect mode is a common and entirely preventable error.

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Three full bundles a month at no cost, no card needed. Speca can also write a resource for a topic we have not built yet, and mark a photo of a student's working against the mark scheme.

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