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.
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 example
From a point 25 m from the foot of a tower, the angle of elevation of the top is \(38^\circ\). Find the height of the tower.
- \(\tan38^\circ=\dfrac{h}{25}\)
- \(h=25\tan38^\circ\)
Answer: \(h=19.5\) m (3 s.f.)
Common mistake
Calculator in radians. Check it shows D (degrees) before you press sin, cos or tan.
On your course
| Course | In the exam |
|---|---|
| AA SL | Not in the booklet: learn it |
| AI SL | Not in the booklet: learn it |
| AI HL | Not in the booklet: learn it |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
Practise and revise
- Practise AI SL right-angled trigonometry questions
- Practise AA SL geometry and right-angled trigonometry questions
- Revise Bearings (AI SL)
- Revise 3D trigonometry (AI SL)
- Print AA SL one-page formula sheet
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?
AA SL: not in the booklet: learn it. AI SL: not in the booklet: learn it. AI HL: not in the booklet: learn it. This comes from our own IB 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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.