Calculadora de Ângulos do Triângulo

The Triangle Angle Calculator solves a common geometry problem: finding the interior angles of a triangle when only the three side lengths are known. Unlike other calculators that require angles or height, this tool uses only side measurements, making it useful when angular measurement tools are unavailable. The calculation is based on the law of cosines, a formula relating triangle sides to the cosine of an angle. Results are given in decimal degrees, which can be converted to degrees, minutes, and seconds if needed.

How it works: you enter the three side lengths (a, b, c) and the calculator applies the law of cosines for each angle. For example, for angle A opposite side a, the formula is cos A = (b² + c² − a²) / (2bc). Then the arccosine function gives the angle in radians, converted to degrees. The process repeats for angles B and C. The sum of the three angles is always 180°, serving as a validity check. If the sides do not form a valid triangle (violating the triangle inequality), an error is displayed.

Use cases include construction projects, where roof or ramp angles need to be determined from linear measurements. It is also useful in surveying to calculate land angles measured with a tape, and in navigation to determine bearings from distances. Students of math and physics can use it to verify exercises or understand practical applications of the law of cosines. Graphic designers or 3D modelers may need precise angles to create geometric shapes.

Important precautions: ensure the side lengths satisfy the triangle inequality, meaning each side must be less than the sum of the other two. Otherwise, the triangle does not exist. Also, the angle accuracy depends on side measurement precision; small errors can cause significant angle differences, especially in very flat triangles. For reliable results, use measurements with at least two decimal places. Remember that the calculator assumes sides in the same unit; do not mix meters and centimeters without conversion.