G6GeometryFoundation & Higher

Trigonometry

Trigonometry uses the ratios sine, cosine and tangent to find missing sides and angles in right-angled triangles. The memory aid SOHCAHTOA tells you which ratio to use.

45 min Video by Maths Genie AQA GCSE Maths

Using SOHCAHTOA to Find a Missing AngleWatch the walkthrough, then read the notes below.

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What you'll learn

Label sides: opposite, adjacent, hypotenuse
Use SOHCAHTOA to find a missing side
Find a missing angle
Know the exact trig values

SOHCAHTOA

Label the sides relative to the angle: $O$ pposite, $A$ djacent, $H$ ypotenuse. Then SOH-CAH-TOA gives the three ratios.

sin = \frac{O}{H}, cos = \frac{A}{H}, tan = \frac{O}{A}

SOH CAH TOA.

1Opposite and hypotenuse → use sin.

sin 30° = \frac{O}{10}

, so

O = 10 sin 30° = 5

cm.

Answer5 cm

Finding angles & exact values

To find an angle, use the inverse trig buttons ( $sin^{- 1}$ , $cos^{- 1}$ , $tan^{- 1}$ ). Learn the exact values, e.g. $sin 30° = \frac{1}{2}$ , $cos 60° = \frac{1}{2}$ , $tan 45° = 1$ .

Tip — Decide which ratio to use from the two sides you have (and the one you want).

Remember these

sin θ = \frac{opp}{hyp}

SOH.

cos θ = \frac{adj}{hyp}

CAH.

tan θ = \frac{opp}{adj}

TOA.

Watch out for these

Mislabelling opposite and adjacent.

Opposite is across from the angle; adjacent is next to it (not the hypotenuse).

Forgetting to use the inverse function to find an angle.

Use sin⁻¹, cos⁻¹ or tan⁻¹ to get the angle.

Key takeaways

Label O, A, H relative to the angle.
SOH CAH TOA picks the right ratio.
Use inverse trig (sin⁻¹ etc.) to find an angle.

Test yourself

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