About this calculator
The SOHCAHTOA Calculator helps find missing sides and angles in right-angled triangles. It is designed for school maths, revision, construction-style sketches, and any situation where you know an angle and a side, or two sides, and need the missing measurement.
SOHCAHTOA calculator method
SOHCAHTOA chooses the trig ratio that connects the known side, the missing side, and the angle. The calculator then rearranges the equation to solve for the missing side or angle.
- SOH: sin(theta) = opposite / hypotenuse
- CAH: cos(theta) = adjacent / hypotenuse
- TOA: tan(theta) = opposite / adjacent
- theta = sin^-1(opposite / hypotenuse), cos^-1(adjacent / hypotenuse), or tan^-1(opposite / adjacent)
How to use the SOHCAHTOA calculator
- Check that the triangle has a right angle.
- Choose whether you are finding a side or an angle.
- Label the opposite, adjacent, and hypotenuse relative to the selected angle.
- Enter the known angle and side, or enter two known sides.
- Choose the missing side where needed.
- Read the ratio used and the rearranged equation.
- Round the answer to the precision required by your question.
Worked examples
Find hypotenuse
Input: Angle 30 degrees, opposite side 5
Calculation: h = 5 / sin(30 degrees)
Result: 10
Find opposite
Input: Angle 40 degrees, hypotenuse 12
Calculation: opposite = 12 x sin(40 degrees)
Result: About 7.71
Find angle
Input: Opposite 6, adjacent 8
Calculation: theta = tan^-1(6 / 8)
Result: About 36.87 degrees
When to use sine, cosine, or tangent
| Known or needed sides | Ratio | Formula |
|---|---|---|
| Opposite and hypotenuse | SOH | sin = opposite / hypotenuse |
| Adjacent and hypotenuse | CAH | cos = adjacent / hypotenuse |
| Opposite and adjacent | TOA | tan = opposite / adjacent |
Why the angle label matters
Opposite and adjacent depend on which acute angle you are using. If you switch to the other acute angle, those two side labels swap. The hypotenuse is always the longest side opposite the right angle.
Common mistakes to avoid
- Mixing degrees and radians
- Most wrong trigonometry answers come from using the wrong angle unit. Check whether the question, calculator, or exam setting is using degrees or radians before comparing results.
- Rounding too early
- Keep extra decimal places during working, then round the final answer. Rounding sine, cosine, or tangent too early can noticeably change a side length or angle.
- Using trig on a non-right triangle
- SOHCAHTOA only applies directly to right-angled triangles. Other triangles may need the sine rule, cosine rule, or a split into right triangles.
Edge cases
- Tangent is undefined where cosine is zero, such as 90 degrees and 270 degrees.
- Inverse sine and inverse cosine only accept inputs from -1 to 1.
- Angles that differ by 360 degrees can have the same sine, cosine, and tangent values.
- A calculated triangle side should not be negative. Recheck the selected side labels if that happens.
Limitations
This calculator is for educational maths support. It uses standard trigonometric formulas and JavaScript Math functions, so results are numerical approximations. For coursework, exams, engineering, surveying, or safety-critical work, follow the required method, units, precision, and marking guidance.
Frequently asked questions
Should I use degrees or radians?
Use the unit given in the question. GCSE-style triangle questions usually use degrees. A-Level maths, calculus, circular motion, and many scientific formulas often use radians.
What does SOHCAHTOA mean?
SOHCAHTOA is a memory aid: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent.
Why is tan 90 degrees undefined?
Tangent is sine divided by cosine. At 90 degrees, cosine is zero, so the division is not defined.
Why do inverse trig calculators sometimes give only one angle?
Inverse trig functions return a principal value. Some trig equations have multiple valid angles over a larger interval, so the calculator result may be one of several possible angles.
Can I use these calculators for GCSE and A-Level revision?
Yes, they are useful for checking working and building confidence. Always practise writing the full method because exam marks often depend on the steps, not just the final number.
Related calculators
- Trigonometry Calculator
- Sine Calculator
- Cosine Calculator