📐 Triangle Solver
Solve any triangle by entering known sides and angles. Calculate missing sides, angles, area, and perimeter using the law of sines and cosines.
About Triangle Solving
Triangle solving is a fundamental skill in geometry and trigonometry that involves finding unknown sides and angles of a triangle when some measurements are known. This process uses mathematical relationships such as the Pythagorean theorem, law of sines, and law of cosines to determine all triangle properties from partial information.
Our triangle solver can handle various triangle types including right triangles, acute triangles, obtuse triangles, and scalene triangles. Whether you're working on homework, designing structures, or solving real-world problems involving triangular shapes, this tool provides accurate calculations for all triangle measurements.
The solver uses advanced algorithms to determine which mathematical laws apply to your specific input combination, ensuring accurate results regardless of which sides and angles you provide. It also calculates additional properties like area and perimeter to give you complete triangle information.
Enter Triangle Information
Enter at least 3 values (including at least one side) to solve the triangle:
Triangle Types and Solving Methods
SSS (Side-Side-Side)
Given: All three sides
Method: Use law of cosines to find all angles
Formula: cos(A) = (b² + c² - a²) / (2bc)
SAS (Side-Angle-Side)
Given: Two sides and included angle
Method: Use law of cosines to find third side, then law of sines for remaining angles
Formula: c² = a² + b² - 2ab·cos(C)
ASA (Angle-Side-Angle)
Given: Two angles and included side
Method: Find third angle, then use law of sines for remaining sides
Formula: a/sin(A) = b/sin(B) = c/sin(C)
AAS (Angle-Angle-Side)
Given: Two angles and non-included side
Method: Find third angle, then use law of sines
Note: Similar to ASA but side is not between the angles
Frequently Asked Questions
What information do I need to solve a triangle?
You need at least three pieces of information about the triangle, with at least one being a side length. Common combinations include: three sides (SSS), two sides and the included angle (SAS), two angles and any side (ASA/AAS), or two sides and a non-included angle (SSA - though this can sometimes have two solutions or no solution).
Can all triangles be solved with any three measurements?
Not always. Some combinations of measurements don't form valid triangles. For example, if you provide three angles that don't sum to 180°, or three sides where one side is longer than the sum of the other two, no triangle can exist. Our solver will detect these cases and provide appropriate error messages.
What are the law of sines and law of cosines?
The law of sines states that a/sin(A) = b/sin(B) = c/sin(C) for any triangle. The law of cosines generalizes the Pythagorean theorem: c² = a² + b² - 2ab·cos(C). These laws allow us to solve triangles when we have partial information about sides and angles.