What Is a SOHCAHTOA Calculator?
A SOHCAHTOA calculator solves right triangles using the three basic trigonometric ratios — sine, cosine, and tangent. SOHCAHTOA is the mnemonic that links each ratio to the sides of a right triangle, and it is the foundation of trigonometry. Enter any combination of a known side and angle (or two sides), and the calculator finds the missing sides and angles, showing which ratio it used.
What SOHCAHTOA Stands For
| Mnemonic | Ratio | Formula |
|---|---|---|
| SOH | Sine | sin θ = Opposite ÷ Hypotenuse |
| CAH | Cosine | cos θ = Adjacent ÷ Hypotenuse |
| TOA | Tangent | tan θ = Opposite ÷ Adjacent |
How to Use the Calculator
- Identify your known values — a side and an angle, or two sides.
- Enter them into the calculator.
- Calculate — see the missing sides and angles with the ratio used.
Choosing the Right Ratio
Label the sides relative to the angle you are working with: the side across from it is the opposite, the side next to it (not the hypotenuse) is the adjacent, and the longest side across from the right angle is the hypotenuse. Then pick the ratio that uses the two sides you know or want.
Worked Example
In a right triangle, if the angle is 30° and the hypotenuse is 10, the opposite side is sin(30°) × 10 = 0.5 × 10 = 5. To find an angle from two sides, use the inverse trig function — for example, θ = tan⁻¹(opposite ÷ adjacent).
Where SOHCAHTOA Is Used
- Geometry and trigonometry classes: solving right triangles.
- Construction and surveying: finding heights and distances.
- Navigation and physics: resolving vectors and angles.
Frequently Asked Questions
What does SOHCAHTOA mean?
It is a mnemonic for the trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent.
How do I find a missing side?
Pick the ratio that involves your known angle and the sides you know and want, then solve. For example, opposite = sin(angle) × hypotenuse.
How do I find a missing angle?
Use the inverse trig functions. For instance, if you know the opposite and adjacent sides, the angle is tan⁻¹(opposite ÷ adjacent).
Does SOHCAHTOA only work for right triangles?
Yes — these ratios apply to right triangles. For non-right triangles, use the law of sines or the law of cosines.
Is this SOHCAHTOA calculator free?
Yes — it is completely free, requires no signup, and solves right triangles step by step.