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Calculator Answers

SOHCAHTOA Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

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.

See also: Right Triangle Calculator, Law of Sines Calculator, and Reference Angle Calculator.

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

SOHCAHTOA Results

Angle θ (Degrees)

36.87°

Solved for hypotenuse side

Opposite side (o)3
Adjacent side (a)4
Hypotenuse (hyp)5
sin(θ) = o / hyp0.6
cos(θ) = a / hyp0.8
tan(θ) = o / a0.75
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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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Right Triangle CalculatorSolve a right triangle from any of two legs, leg + hypotenuse, leg + acute angle, or hypotenuse + acute angle. Returns all sides, both acute angles, area, and perimeter.Law of Sines CalculatorSolve any triangle using a/sin(A) = b/sin(B) = c/sin(C) with AAS, ASA, and SSA cases, including the ambiguous case.Reference Angle CalculatorFind the positive acute reference angle for any angle in degrees or radians (including fractions of pi) with a unit circle visualizer and step-by-step rules.

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.