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SOHCAHTOA Calculator
Last updated: June 17, 2026
A SOHCAHTOA calculator is a right-triangle trigonometry solver that computes unknown side lengths and angles using the basic trig ratios: Sine (Opposite/Hypotenuse), Cosine (Adjacent/Hypotenuse), and Tangent (Opposite/Adjacent). By providing any two side lengths, the calculator determines the third side using the Pythagorean theorem, and computes the angles and trig values. It is a fundamental tool for introductory geometry and trigonometry students.
Solve right triangles easily using SOHCAHTOA trigonometric ratios. Input any two side values to find all sides, angles, and trigonometric ratios.
Quick Answer
Solve a right triangle using SOHCAHTOA. Input any two of opposite, adjacent, or hypotenuse to find the remaining side, angle, and sine, cosine, and tangent ratios.
Right Triangle Sides
Enter exactly **two** values to solve the triangle.
Side opposite to angle θ. · e.g. 3
Side adjacent to angle θ (excluding hypotenuse). · e.g. 4
The longest side of the right triangle. · e.g. 5
Angle θ (Degrees)
36.87°
Solved for hypotenuse side
Examples
3-4-5 Triangle
opposite = 3 · adjacent = 4 — Hypotenuse = 5 · Angle θ = 36.87°
Solve for Adjacent
opposite = 5 · hypotenuse = 13 — Adjacent = 12 · Angle θ = 22.62°
How it works
Trig Definitions
In any right triangle, the trig functions are defined relative to one of the acute angles (θ):
- Sine (SOH): sin(θ) = opposite / hypotenuse
- Cosine (CAH): cos(θ) = adjacent / hypotenuse
- Tangent (TOA): tan(θ) = opposite / adjacent
Pythagorean Theorem
To find the missing side, the calculator uses the Pythagorean relation:
a² + o² = hyp²
Disclaimer
For educational purposes. Verify results for critical applications.
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Frequently asked questions
SOHCAHTOA is a mnemonic helper to remember trig definitions: Sine = Opposite / Hypotenuse (SOH), Cosine = Adjacent / Hypotenuse (CAH), and Tangent = Opposite / Adjacent (TOA).
You need exactly two values. Entering any two side lengths allows the Pythagorean theorem to solve the third side, and trig ratios to solve for the angles.
The hypotenuse is the longest side opposite the right angle. The opposite side is directly across from the target angle θ. The adjacent side is next to angle θ but is not the hypotenuse.
In a right triangle, the hypotenuse must be the longest side. If you enter a hypotenuse that is shorter than or equal to the opposite or adjacent side, the triangle is geometrically impossible, resulting in a square root of a negative number.
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