Right Triangle Side and Angle Calculator

Every right triangle consists of a 90-degree right angle, two acute angles, and three sides: the hypotenuse (the longest side opposite the right angle) and two legs. This calculator uses core geometric principles like the Pythagorean theorem and fundamental trigonometric ratios to determine unknown values. When two dimensions are known—such as one side and one angle, or two sides—the tool applies formulas such as c = sqrt(a² + b²), tan(alpha) = a/b, and the angle sum rule where alpha + beta = 90 degrees to instantly compute the complete geometry of the triangle.

Imagine you have a right triangle where leg a is 3 inches long and leg b is 4 inches long. To find the hypotenuse (c) and the acute angles, we apply the Pythagorean theorem. First, square both legs: 3 squared is 9, and 4 squared is 16. Adding them together gives 25. Taking the square root of 25 yields a hypotenuse of 5 inches. Next, to find the angle opposite to leg a, we use the tangent ratio: tan(alpha) = 3/4 = 0.75. Taking the inverse tangent of 0.75 gives approximately 36.87 degrees. Finally, the remaining angle is simply 90 minus 36.87, which equals 53.13 degrees.

Always verify your input values and ensure your units of measurement remain consistent throughout the entire calculation process. Keep in mind that you must always know at least two unique values—excluding the 90-degree right angle—to successfully solve for the rest of the triangle. Double-check whether your angle inputs are in degrees or radians before running computations to prevent severe scaling errors in your results.