Oblique Triangle Calculator - Solve Sides, Angles, Area

An oblique triangle calculator is a geometry tool that solves for every missing side and angle of a triangle that does not contain a 90-degree angle. It accepts the five standard input cases, applies the law of sines or the law of cosines, and returns the complete triangle plus area, perimeter, inradius, and circumradius.

• • Trigonometry homework: Walk through AAS, ASA, and SAS problems by reading the missing side and angle from the same output.
• • Surveying and roof framing: Find the third side of a triangular lot or roof face from two measured sides and the angle between them, then take area straight into a takeoff sheet.
• • Navigation and bearings: Convert a measured distance and bearing plus a second distance into the closing side and interior angles of the triangle on a chart.
• • Physics and engineering: Resolve force or velocity triangles from two known sides and the included angle, then read the third side and the opposite angles.

A single length unit on all three side inputs is enough. The law of sines and the law of cosines only need the ratios, so the area, inradius, and circumradius come back in matching units.

If the triangle has a 90-degree angle, the dedicated Right Triangle Calculator handles that special case with the Pythagorean theorem and a simpler side-solver form.

The calculator detects the input case from the non-zero values you enter, then runs the law of sines or the law of cosines to solve for the missing sides and angles. The solved triangle is then used to compute area, perimeter, inradius, and circumradius.

• a, b, c: Side lengths opposite angles A, B, and C respectively.
• A, B, C: Interior angles in degrees at the three vertices. They sum to 180 for any valid triangle.
• sin(C), cos(C): Sine and cosine of the included angle C, in radians, used by the law of sines and the law of cosines.
• s: Semi-perimeter used in the inradius formula: r = area / s. Equal to perimeter / 2.

According to Wolfram MathWorld, the law of sines says the ratio of a side to the sine of its opposite angle is the same for all three sides of any triangle.

When the same SAS inputs only need the area, the height against side a, and the third side, the dedicated Area Oblique Triangle Calculator produces that subset of the result in a single page.

These four ideas decide which rule the calculator applies and how to read the output.

When the included angle is known, the law of cosines is the cleanest path. When one side and its opposite angle are known, the law of sines fills in the rest in two or three short steps. Most exercises are designed so that exactly one rule applies.

The ambiguous case is the one place where the law of sines alone is not enough. Drawing the perpendicular from the vertex opposite the given side is the same logic the calculator runs to decide whether one or two triangles fit the inputs.

According to Wolfram MathWorld, the three interior angles of any triangle sum to 180 degrees, and a triangle with no right angle is called oblique.

If the same worksheet mixes input cases, the general-purpose Triangle Calculator reads the input set, picks the right rule, and returns the solved triangle without changing tools.

Pick the input case that matches the values you have, enter only those values, and read the solved triangle from the results panel.

1. 1 Choose the input case: Use the dropdown to select SSS, SAS, SSA, ASA, or AAS based on which sides and angles you already know.
2. 2 Enter the known sides and angles: Fill in only the fields that match your input case. Leave every unknown field at 0 so the calculator does not treat it as a constraint.
3. 3 Check the unit consistency: Use the same length unit on all three side inputs. Mixed units will silently produce a wrong area and a wrong inradius.
4. 4 Read the solved triangle: Read the three solved sides, the three solved angles, the area, the perimeter, the inradius, and the circumradius in the results panel.
5. 5 Handle the ambiguous case: If SSA produces two solutions, the calculator labels them Solution 1 and Solution 2. Pick the one that fits the real geometry.
6. 6 Reset for a new triangle: Use the Reset button to clear the form and start over with a new problem.

Suppose a roof face has two measured edges of 7 feet and 9 feet meeting at 60 degrees. Pick SAS, enter a = 7, b = 9, C = 60, leave the other fields at 0. The calculator returns c = 8.19 feet, A = 47.79, B = 72.21, area = 27.28 square feet, perimeter = 24.19 feet, inradius = 2.26 feet, circumradius = 4.73 feet.

When only the vertex labels and ratios are known, the ABC Triangle Calculator reads three labeled sides or angles and returns the rest of the triangle with the same law of sines and law of cosines steps.

A single page that handles every standard input case is faster than keeping three or four reference tables open at the same time.

• • Five input cases in one tool: SSS, SAS, SSA, ASA, AAS run on the same form.
• • Ambiguous case handled explicitly: The SSA case returns both valid triangles when they exist.
• • Complete secondary outputs: Area, perimeter, inradius, circumradius come back with the solved sides and angles.
• • Built-in validation: Triangle inequality violations, angle sums over 180, and zero inputs are caught in one guidance message.
• • Same output units as input units: Use one length unit on every side input. Area comes back in square units of that length.

The calculator returns enough information to cross-check the same problem with a textbook answer key. The area, inradius, and circumradius are the proof that the same triangle satisfies every other geometric identity.

When the exercise is specifically the AAS case, the focused AAS Triangle Calculator only needs two angles and a non-included side to return the solved triangle.

The law of sines and the law of cosines are exact, but the way the inputs are read decides whether the result is the triangle you actually want.

• • The calculator assumes planar (flat) triangles. Spherical or surveying triangles over very long distances need spherical trigonometry instead.
• • The inradius and circumradius outputs assume the same length unit on all three sides. Mixing units will silently change those two numbers in particular.

If the calculator returns a guidance message, the most productive next step is to check which fields are non-zero. A stray zero in the middle of a side input can flip the case from SSS to something the calculator cannot solve.

For high-precision work, the law of cosines is more numerically stable than the law of sines for nearly collinear triangles, which is why the SSS path uses it.

According to Wolfram MathWorld, the law of cosines generalizes the Pythagorean theorem to oblique triangles.

If the only knowns are two angles and the side between them, the ASA Triangle Calculator applies the 180-degree angle sum and the law of sines without a law of cosines step.