Find missing sides and angles with clear steps. Handle validations, exports, and plotted triangle geometry. Use clean inputs for fast and accurate triangle solving.
Enter any valid law of sines setup. Best results come from two angles with one side, or one opposite pair with another side.
| Example | Known Values | Computed Values |
|---|---|---|
| Triangle 1 | A = 42°, B = 63°, a = 8 | C = 75°, b = 10.653, c = 11.548 |
| Triangle 2 | A = 35°, a = 7, b = 9 | Possible SSA case with one or two solutions |
| Triangle 3 | B = 48°, C = 67°, c = 14 | A = 65°, a and b solved from the ratio |
The law of sines states that the ratio of each side to the sine of its opposite angle stays equal in the same triangle.
a / sin(A) = b / sin(B) = c / sin(C)
Use it when you know two angles and one side, or one side-angle pair plus another side. In SSA cases, two valid triangles may exist. This calculator checks for that ambiguous result and lists each valid solution separately.
This calculator helps solve triangles by using opposite side-angle relationships. It is useful in geometry classes, surveying tasks, navigation work, and technical drawing exercises. The layout keeps everything in one vertical flow, so the result appears right below the header and above the form as requested.
You can enter angles A, B, and C with sides a, b, and c. Sides use the standard naming rule. Side a lies opposite angle A. Side b lies opposite angle B. Side c lies opposite angle C. This pairing is essential because the law compares each side directly with its opposite angle.
The calculator supports common AAS and ASA situations. It also handles the well-known SSA ambiguous case. In that case, one input set can produce two different valid triangles. When that happens, the result table shows both solutions, and each one gets its own step list and plotted triangle.
Validation is included to catch unrealistic inputs. Angles must stay positive. Any known angle pair must total less than 180 degrees. If all angles are supplied, they must sum to 180 degrees. If all sides and angles are supplied, the calculator checks whether they remain consistent with the sine relation.
The plotted graph gives a quick visual check of the triangle shape. This is useful for spotting narrow, tall, or wide triangles. The export tools also help with assignments, worksheets, and saved records. Use CSV for spreadsheet storage and PDF for a simple print-friendly summary.
It finds missing sides or angles in a triangle when you know a usable opposite side-angle relationship. It is especially helpful for ASA, AAS, and SSA cases.
Yes. If the data allows two valid triangles, both results are shown. Each solution includes its own angles, sides, area, perimeter, steps, and graph trace.
Use two angles with one side, or use one side-angle pair with another side. Those are the most direct setups for the sine relation.
Your known values may be inconsistent. Common causes include angle sums reaching or exceeding 180 degrees, negative values, or an SSA setup that cannot form a triangle.
Yes. Choose radians from the angle unit menu. The calculator converts inputs internally and displays the solved angles back in the selected unit.
They give a fuller triangle summary after solving. Perimeter adds all sides. Area is computed from solved measurements, which helps with practical geometry work.
No. The graph is a visual aid. It helps confirm triangle shape and compare multiple SSA outcomes, but the numeric solution does not depend on plotting.
Yes. Use the CSV button for tabular data and the PDF button for a printable summary. Both appear when a valid result is available.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.