This triangle calculator solves a whole triangle from partial information, giving you every side, every angle, the area and the perimeter. It handles the two most common cases. The first is three sides, known as SSS, where you measure all three edges and want the angles and area, which is exactly the situation when you have a triangular section of land or material and need to know its angles. The second is two sides and the angle between them, known as SAS, where the third side and the remaining angles are found for you. The calculator works with any triangle, not just right angled ones, by using the law of cosines to recover missing sides and angles and either Heron's formula or the half a b sine C rule for the area. It checks that your inputs can actually form a triangle first, applying the triangle inequality for three sides and requiring a sensible included angle for the SAS case, and tells you clearly when no valid triangle exists. Angles are returned in degrees. This is a staple tool for geometry and trigonometry study, as well as practical trades work in carpentry, surveying and design where triangles are everywhere. Choose your method, enter what you know, and the full solution appears as you type.
For three sides, each angle comes from the law of cosines, for example angle A is the inverse cosine of b squared plus c squared minus a squared, over two b c. For two sides and the included angle, the third side comes from the law of cosines and the area from half a b times the sine of the included angle. The area for three sides uses Heron's formula.
A triangle with sides 5, 6 and 7 has angles of about 44.4, 57.1 and 78.5 degrees, a perimeter of 18, and an area of about 14.7 square units found from Heron's formula.
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