Oblique Triangle
Solve any oblique triangle with SSS, SAS, ASA, or AAS inputs. Free online triangle solver computes all sides, angles, area, and perimeter instantly using the law of sines and cosines.
About This Calculator
This oblique triangle calculator solves any triangle that does not contain a right angle using four standard input methods: SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side), and AAS (two angles and a non-included side). Whether you are a student studying trigonometry, an engineer working on structural analysis, or a surveyor calculating land measurements, this tool provides complete triangle solutions including all three side lengths, all three angle measures, area, and perimeter.
The calculator applies the law of cosines (c^2 = a^2 + b^2 - 2ab·cos(C)) for SSS and SAS modes where all three sides or two sides with an included angle are known. For ASA and AAS modes, the law of sines (a/sin(A) = b/sin(B) = c/sin(C)) is used along with the triangle angle sum property (A + B + C = 180 deg). Area is computed using Heron's formula for SSS inputs and the SAS area formula (Area = 1/2ab·sin(C)) for other modes.
All four supported methods (SSS, SAS, ASA, AAS) uniquely determine a triangle. The ambiguous SSA case is not supported because it can produce zero, one, or two possible triangles. If you are unsure which mode to use, choose the one that matches the values you already know -- you only need three pieces of information (side lengths and/or angle measures) to solve the entire triangle.
Results are displayed with two decimal precision for side lengths, angles in degrees, and area in square units. The calculator also validates input using the triangle inequality theorem for SSS inputs and angle sum constraints for ASA and AAS inputs to ensure mathematically valid triangles.
Frequently Asked Questions
What is an oblique triangle?
An oblique triangle is any triangle that does not contain a 90-degree (right) angle. It can be acute (all angles less than 90 degrees) or obtuse (one angle greater than 90 degrees). Oblique triangles are solved using the law of sines and the law of cosines rather than the Pythagorean theorem used for right triangles.
What is the difference between SSS, SAS, ASA, and AAS?
These are the four valid combinations for solving an oblique triangle. SSS (Side-Side-Side) uses all three side lengths. SAS (Side-Angle-Side) uses two sides and the angle between them. ASA (Angle-Side-Angle) uses two angles and the side between them. AAS (Angle-Angle-Side) uses two angles and a side not between them. Each combination uniquely determines a triangle.
What formulas does this oblique triangle calculator use?
The calculator uses the law of cosines (c^2 = a^2 + b^2 - 2ab·cos(C)) for SSS and SAS modes, the law of sines (a/sin(A) = b/sin(B) = c/sin(C)) for ASA and AAS modes, Heron's formula for area in SSS mode, and the formula Area = 1/2ab·sin(C) for area in other modes. The perimeter is always the sum of all three sides.
Can all three sides form a valid triangle?
For three side lengths to form a valid triangle, they must satisfy the triangle inequality theorem: the sum of any two sides must be greater than the third side. If your sides violate this rule, the calculator will show an error message. For example, sides of 1, 2, and 4 cannot form a triangle because 1 + 2 is not greater than 4.
What is the SSA (or ASS) case and why isn't it supported?
SSA (Side-Side-Angle) is not supported because it does not uniquely determine a triangle. Depending on the values, there may be zero, one, or two possible triangles. This is known as the ambiguous case. To avoid incorrect results, use ASA or AAS instead by entering a different combination of known angles and sides.
How accurate are the results?
The calculator uses JavaScript double-precision floating-point arithmetic and rounds results to two decimal places. For most practical purposes in education, construction, and engineering, this provides sufficient accuracy. Trigonometric functions are computed using standard Math library routines accurate to approximately 15 significant digits.
Can I share my calculation results?
Yes. After calculating, the input values are saved in the URL as query parameters. You can copy the URL from your browser's address bar and share it with anyone. When they open the link, the calculator will automatically populate the same values and compute the results.
What is the law of sines and law of cosines?
The law of sines states that the ratio of a side length to the sine of its opposite angle is constant for all three sides of a triangle: a/sin(A) = b/sin(B) = c/sin(C). The law of cosines relates a side length to the other two sides and the angle between them: c^2 = a^2 + b^2 - 2ab·cos(C). Together these formulas can solve any oblique triangle.