SOH CAH TOA formula: sin = opp/hyp, cos = adj/hyp, tan = opp/adj

The SOH CAH TOA formula is sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.

\(\displaystyle \sin\theta=\frac{\text{opp}}{\text{hyp}}\) \(\displaystyle \cos\theta=\frac{\text{adj}}{\text{hyp}}\) \(\displaystyle \tan\theta=\frac{\text{opp}}{\text{adj}}\)

What each letter means

\(\theta\) the angle you are using (not the right angle)
\(\text{opp}\) the side opposite θ
\(\text{adj}\) the side next to θ that is not the hypotenuse
\(\text{hyp}\) the hypotenuse, opposite the right angle

When to use it

In a right-angled triangle, when the problem involves an angle and two sides: heights from angles of elevation, slopes, bearings.

Worked examples

1. A right-angled triangle has hypotenuse 15 cm and an angle of \(28^\circ\). Find the side opposite the angle.

\(\sin28^\circ=\dfrac{\text{opp}}{15}\)
\(\text{opp}=15\sin28^\circ\)

Answer: 7.04 cm (3 s.f.)

2. The opposite side is 7 cm and the adjacent side is 10 cm. Find the angle, to 1 decimal place.

\(\tan\theta=\dfrac{7}{10}\)
\(\theta=\tan^{-1}0.7\)

Answer: \(\theta=35.0^\circ\)

Common mistake

Calculator in radians. Check it shows D (degrees) before you press sin, cos or tan.

On your course

Course	In the exam
Edexcel 4MA1 (Higher)	Not given: learn it
Cambridge 0580	Not given: learn it

From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).

Practise and revise

Practise 4MA1 right-angled trigonometry questions
Practise 0580 right-angled trigonometry questions
Revise Geometry and trigonometry notes
Print Edexcel 4MA1 (Higher) one-page formula sheet

SOH CAH TOA (right-angled trigonometry) formula card: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. IGCSE Math Revision — SOH CAH TOA (right-angled trigonometry) formula card. Download the card (PNG) to save or print it.

Questions

What is the SOH CAH TOA formula?

The SOH CAH TOA formula is sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. θ: the angle you are using (not the right angle); opp: the side opposite θ; adj: the side next to θ that is not the hypotenuse; hyp: the hypotenuse, opposite the right angle.

Is the SOH CAH TOA (right-angled trigonometry) given in the exam?

Edexcel 4MA1 (Higher): not given: learn it. Cambridge 0580: not given: learn it. This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.

What does SOH CAH TOA stand for?

Sin = Opposite ÷ Hypotenuse, Cos = Adjacent ÷ Hypotenuse, Tan = Opposite ÷ Adjacent. It only works in right-angled triangles.

Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.