Solve any triangle using our comprehensive calculator. Whether you know three sides (SSS), two sides and an angle (SAS/SSA), or two angles and a side (ASA/AAS), our tool will calculate all missing properties including sides, angles, area, and perimeter with step-by-step explanations.
✨ Beautiful geometry made simple
c² = a² + b² - 2ab·cos(C)
Use when you know three sides (SSS) or two sides and the included angle (SAS). This law generalizes the Pythagorean theorem for all triangles.
a/sin(A) = b/sin(B) = c/sin(C)
Use when you know two angles and any side (ASA/AAS) or two sides and a non-included angle (SSA). Perfect for finding unknown sides or angles.
Calculate roof angles, determine building layouts, and solve structural engineering problems.
Measure land boundaries, calculate distances, and determine property dimensions accurately.
Perfect for students learning trigonometry, geometry, and solving homework problems.
Our triangle calculator supports all five main methods: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), AAS (two angles and non-included side), and SSA (two sides and non-included angle). Each method uses different geometric principles to solve for the unknown triangle properties.
The SSS method uses the Law of Cosines to find all angles when three sides are known. It first checks the triangle inequality (sum of any two sides must be greater than the third side) to ensure a valid triangle exists, then calculates each angle using the formula: cos(A) = (b² + c² - a²) / (2bc).
ASA (Angle-Side-Angle) uses two angles and the side between them, while AAS (Angle-Angle-Side) uses two angles and a side that's not between them. Both methods first calculate the third angle (since angles sum to 180°), then use the Law of Sines to find the remaining sides.
The SSA (Side-Side-Angle) method can be ambiguous because given two sides and a non-included angle, there might be two different triangles that satisfy these conditions, one solution, or no solution at all. This is known as the 'ambiguous case' in trigonometry. Our calculator checks for validity and provides the primary solution when one exists.
Our calculator uses precise mathematical formulas (Law of Cosines and Law of Sines) and displays results rounded to two decimal places. The calculations are performed using JavaScript's built-in Math functions, providing high accuracy suitable for most practical applications including homework, engineering, and construction projects.
You can enter side lengths in any unit (inches, centimeters, meters, feet, etc.) as long as you're consistent across all sides. Angles must be entered in degrees. The calculator will maintain the same units for the results - if you input sides in centimeters, the area will be in square centimeters.
The area is calculated using different formulas depending on the input method. For SAS, it uses Area = 0.5 × a × b × sin(C). For other methods, it may use Heron's formula or the standard Area = 0.5 × base × height formula after calculating all sides and angles.
The calculator validates your inputs and will show an error if the measurements don't form a valid triangle. Common issues include violating the triangle inequality (where the sum of two sides is less than or equal to the third side) or entering angles that sum to more than 180 degrees.
Yes! Our calculator works perfectly for right triangles (triangles with a 90° angle). You can use any of the supported methods - for example, if you know two sides of a right triangle, you can use SSA method with the 90° angle, or SAS if you know the two sides that form the right angle.
Click the 'Steps' button to see the mathematical approach used for your selected method. This shows which formulas are applied (Law of Cosines, Law of Sines, etc.) and helps you understand the geometric principles behind the calculations. This is especially helpful for students learning trigonometry.
The Law of Cosines relates the lengths of sides to the cosine of one angle and is used when you know three sides (SSS) or two sides and the included angle (SAS). The Law of Sines relates the ratios of sides to the sines of their opposite angles and is used when you know two angles and a side (ASA/AAS) or in some SSA cases.
Absolutely! This triangle calculator is perfect for practical applications like surveying, construction, carpentry, and engineering. It can help you calculate roof angles, determine property boundaries, plan construction layouts, or solve any real-world problem involving triangular measurements.
The calculator can handle a wide range of triangle sizes, from very small (millimeters) to very large (kilometers) measurements. However, extremely large numbers might lose precision due to JavaScript's floating-point limitations. For most practical applications, the calculator provides more than sufficient accuracy.
Choose the method based on what information you have: SSS if you know all three sides, SAS if you know two sides and the angle between them, ASA if you know two angles and the side between them, AAS if you know two angles and any side, and SSA if you know two sides and an angle opposite one of them.
Yes! Our calculator handles all types of triangles: acute (all angles less than 90°), right (one 90° angle), and obtuse (one angle greater than 90°). The mathematical formulas used (Law of Cosines and Law of Sines) work for all triangle types, and the calculator will correctly identify and solve obtuse triangles.