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Connect an angle to the sides of a right triangle — sin, cos, and tan.
Give one acute angle and one known side; Axiom finds the other two sides.
Choose Find sides for an acute angle and one known side, or Find angle for two known sides. Select the known side’s role or the appropriate sine, cosine, or tangent ratio, enter positive lengths, and press Calculate; angles are in degrees.
SOH CAH TOA means sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent. Rearrange a ratio to find a side, or apply its inverse function to find an angle. Opposite and adjacent depend on the chosen acute angle; the hypotenuse is always opposite the right angle.
Choose Find sides, enter 30°, select Opposite, and enter 3. Hypotenuse = 3/sin 30° = 6; adjacent = 6 cos 30° ≈ 5.196152423. The other acute angle is 60°.
Choose Find angle and tan — TOA. Enter opposite 3 and adjacent 4. tan θ = 3/4 = 0.75, so θ = tan⁻¹(0.75) ≈ 36.86989765°; the other acute angle is approximately 53.13010235°.
Use the ratio containing the two sides you know: opposite and hypotenuse for sine, adjacent and hypotenuse for cosine, or opposite and adjacent for tangent.
No. These ratios are applied to right triangles here. A non-right triangle may require the sine rule or cosine rule, which this calculator does not implement.
No. Convert radians to degrees by multiplying by 180/π before entering an angle. Find sides expects an angle strictly between 0° and 90°.
In a nondegenerate right triangle it is the longest side, and the angle opposite a leg is acute. Equal leg and hypotenuse inputs would mean a 0° or 90° angle, so this calculator asks for a genuinely shorter side instead of reporting a degenerate triangle.
For two known sides without an angle, use the Pythagorean tool. The trigonometry lesson explains side labels and ratio choice, while the General Calculator can check individual degree-mode functions. Related tools: Pythagorean Theorem Calculator, General Calculator. Read the Trigonometry (SOH CAH TOA) lesson or practice trigonometry (soh cah toa) to build confidence without relying on a calculator.