Trigonometry Calculator

Right-triangle trigonometry describes the relationship between two acute angles and three side lengths. One angle is fixed at 90 degrees, so the other two angles are complementary and add to 90 degrees. The hypotenuse is always opposite the right angle and is the triangle's longest side. The terms opposite and adjacent depend on which acute angle, commonly called θ, is being studied. The familiar mnemonic SOHCAHTOA summarizes the primary ratios. Sine of θ equals opposite divided by hypotenuse. Cosine equals adjacent divided by hypotenuse. Tangent equals opposite divided by adjacent. When the two legs are known, tangent provides the target angle through the inverse function θ = arctan(opposite / adjacent). The remaining acute angle is 90° - θ. The hypotenuse follows from the Pythagorean theorem: h² = opposite² + adjacent². Taking the positive square root gives h because geometric lengths must be positive. This calculator uses a stable hypotenuse operation that avoids unnecessary overflow for ordinary measurements, then reports each result to four decimal places. All three side lengths share the same unit, whether the inputs represent centimetres, metres, feet, or another consistent unit. Correct labeling matters. Imagine standing at angle θ and looking into the triangle. The leg across from you is opposite; the non-hypotenuse leg touching you is adjacent. If you choose the other acute angle as θ, those two labels swap. The calculated pair of acute angles also swaps, while the hypotenuse remains unchanged. Right-triangle calculations appear in roof pitch, ramp design, land surveying, navigation, forces, shadows, heights, and vector components. They assume the triangle truly contains a 90-degree angle and that the input lengths are measured consistently. For construction or safety-critical engineering, account for measurement tolerances and applicable design standards rather than relying only on rounded calculator output. This focused solver accepts the two legs because that pair always determines one unique right triangle. If your known values instead include a hypotenuse or an angle, rearrange sine, cosine, or tangent to obtain a leg first. The displayed result then offers a quick check of the complete geometry.