Trigonometry (SOH CAH TOA)

MathematicsAQAEdexcelGCSEUnit: Geometry & Measures
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The basics

Beyond Pythagoras

Beyond Pythagoras

Pythagoras helps find sides, but what if you need to find an ANGLE? Or what if you know an angle and only ONE side? That's where trigonometry comes in. The three ratios (sine, cosine, tangent) connect angles and sides in right-angled triangles.

Visual: SOH CAH TOA

Diagram showing SOH CAH TOA trigonometry ratios. A right triangle labelled with Opposite, Adjacent, and Hypotenuse from angle θ. SOH: sin θ = O/H, CAH: cos θ = A/H, TOA: tan θ = O/A
Spotlight
The Labels (CRUCIAL!)

First, label your triangle from the angle you're working with:

Now try it yourself

Quiz · Question 1 of 19

Which trigonometric ratio connects the opposite side and the hypotenuse in a right-angled triangle?

Tap an answer to check it

This topic in real past papers

Every real exam question we've found on trigonometry (soh cah toa), with a full worked answer.

AQA Paper 2

All four sittings we have full papers for combine Pythagoras or right-angled trigonometry with a second calculation, an area, a perimeter or a further angle, in a composite shape made of two joined pieces.

4 marks

AQA Paper 3

Two of the four sittings we have full papers for give a right-angled triangle and ask for a missing angle or a missing side to be found using trigonometry.

3 marks

Edexcel Paper 2

All three sittings we have full papers for test trigonometry to find a missing length or angle, and June 2019 tests it twice: once in a simple right-angled triangle and once inside a 3D solid.

4 marks

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