Right-angled triangle trigonometry calculator (SOHCAHTOA)
Enter any two known values from a right-angled triangle — two sides, or one side and an acute angle — and this calculator finds everything else. It names the ratio it used (sin, cos or tan), shows the rearrangement, and gives all three sides, both acute angles and the area, so you can check every line of your own working.
Enter any two values — leave the rest blank
Opposite and adjacent are named relative to angle A. The hypotenuse is opposite the right angle.
A = 36.87° · B = 53.13°
Opposite: 6 · Adjacent: 8 · Hypotenuse: 10
Area: ½ × opp × adj = 24
Working
- h = √(opp² + adj²) = √(6² + 8²) = 10
- tan A = opp ÷ adj = 6 ÷ 8, so A = tan⁻¹(0.75) = 36.87°
- The angles in the triangle add to 180°, so B = 90° − 36.87° = 53.13°
The method behind it
- sin θ = opp ÷ hyp, cos θ = adj ÷ hyp, tan θ = opp ÷ adj.
- Finding an angle from two sides means using sin⁻¹, cos⁻¹ or tan⁻¹.
- The two acute angles always add to 90°, and a² + b² = c².
How to use this tool
1. Label the triangle
The hypotenuse is the longest side, opposite the right angle. Opposite and adjacent are named relative to angle A, the acute angle you are working with.
2. Enter any two values
Type two of: opposite, adjacent, hypotenuse or angle A in degrees. Leave everything else blank.
3. Read the ratio and working
The steps show which of sin, cos or tan applies and how it was rearranged to reach the unknown.
Frequently asked questions
What does SOHCAHTOA stand for?
Sin = Opposite ÷ Hypotenuse, Cos = Adjacent ÷ Hypotenuse, Tan = Opposite ÷ Adjacent. Pick the ratio that uses the two sides you know or need.
When do I use sin⁻¹, cos⁻¹ or tan⁻¹?
Use the inverse function when you are finding an angle from two known sides. For example if you know the opposite and the hypotenuse, the angle is sin⁻¹(opposite ÷ hypotenuse).
Does SOHCAHTOA work in non-right-angled triangles?
No. For triangles without a right angle you need the sine rule or the cosine rule — use our sine and cosine rule calculator instead.
How should I round trigonometry answers?
Keep full accuracy in your calculator and only round the final answer, usually to 3 significant figures for sides and 1 decimal place for angles unless the question states otherwise.
Practise this properly, not just once
A solver gives you the answer; exam marks come from the working. MathsGradeUp pairs exam-board questions with step-by-step feedback and revision notes on the exact topics you keep dropping marks on.