Example Data Table
| Case | Known Values | Expected Use |
|---|---|---|
| SSS | a = 7, b = 9, c = 11 | Find all angles, area, and centers. |
| SAS | a = 10, b = 14, C = 46 | Find the included side and remaining angles. |
| ASA or AAS | A = 42, B = 68, a = 12 | Scale the triangle from one known side. |
| SSA | A = 38, a = 9, b = 12 | Check whether two valid triangles exist. |
Formula Used
Law of Cosines: a² = b² + c² - 2bc cos(A). Similar forms solve b, c, and angles.
Law of Sines: a / sin(A) = b / sin(B) = c / sin(C). It solves ASA, AAS, and SSA cases.
Heron's Formula: area = √[s(s - a)(s - b)(s - c)], where s = (a + b + c) / 2.
Trigonometric Area: area = 1/2 bc sin(A). Equivalent forms use other included angles.
Heights: ha = 2 area / a. The same rule applies to b and c.
Medians: ma = 1/2 √(2b² + 2c² - a²). Other medians follow by symmetry.
Angle Bisectors: la = √[bc(1 - a² / (b + c)²)].
Radii: inradius r = area / s. Circumradius R = a / [2 sin(A)].
How to Use This Calculator
- Label the triangle sides as a, b, and c.
- Match angles A, B, and C opposite those sides.
- Enter any valid SSS, SAS, ASA, AAS, or SSA set.
- Choose decimal places and write the length unit.
- Press the calculate button.
- Review every solution, especially for SSA data.
- Use the CSV or PDF button to save the result.
Advanced Oblique Triangle Analysis
A non right triangle has no angle fixed at ninety degrees. It can be acute or obtuse. Many real measurements create this shape. Survey paths, roof faces, brackets, fields, maps, and classroom problems often use it. This calculator accepts common input sets. You can enter three sides, two sides with an included angle, two angles with a side, or the ambiguous side side angle case.
Why This Method Helps
The tool solves the complete triangle first. It then reports angles, missing sides, perimeter, area, semiperimeter, heights, medians, angle bisectors, inradius, circumradius, and exradii. These outputs give more than a simple answer. They support checking, drawing, and estimating material needs. They also help students see how several formulas connect.
Working With Real Data
Non right triangle data can be incomplete or noisy. For that reason, the calculator checks triangle inequality, angle totals, and possible ambiguous results. The side side angle case may produce zero, one, or two valid triangles. When two solutions exist, both are shown separately. This is useful in navigation and layout work, where the same measurements can describe different shapes.
Practical Uses
Use the calculator for trigonometry homework, site measurement, frame design, garden planning, and map scaling. It is also useful when checking handwritten work. The downloadable CSV file works well for spreadsheets. The PDF report gives a simple record for notes, reviews, or client documents.
Accuracy Notes
Angles are entered in degrees. Internally, trigonometric functions use radians. Rounded values are shown by your selected precision. Very small rounding differences can appear near flat or nearly right triangles. Always keep original field measurements when final safety, legal, or engineering decisions depend on the result.
Interpreting the Results
Start with the solved sides and angles. Then review area and height values. A large height shows a tall narrow shape. A small height can show a flattened shape. Compare medians and bisectors when you need internal layout lines. Radius values describe related circles. The inradius fits inside the triangle. The circumradius passes through all vertices. Exradii are useful in advanced geometry checks. The warning notes help catch impossible entries before export. Use them to confirm sketches before sharing clear results with students, teammates, or clients later.
FAQs
What is a non right triangle?
It is a triangle without a ninety degree angle. It may be acute or obtuse. The calculator still warns if entered data creates a right triangle.
Which input types are supported?
It supports SSS, SAS, ASA, AAS, and SSA. The SSA case may return two possible triangles when measurements allow an ambiguous result.
Can I enter all sides and angles?
Yes. The calculator solves from the strongest valid set, then compares extra entries. Warnings show when supplied values disagree with the solved triangle.
Why does SSA show two solutions?
SSA can match two different angle layouts. The law of sines creates an acute angle and a possible obtuse supplement. Both are valid only when angle totals stay below 180 degrees.
What units should I use?
Use any consistent length unit. Enter all sides in the same unit. Area is then reported in square units based on that label.
How is area calculated?
The calculator uses Heron's formula after the sides are known. This keeps the area method consistent across SSS, SAS, ASA, AAS, and SSA inputs.
Can this help with surveying?
Yes. It can check sloped or oblique layouts. For official work, confirm field measurements and local standards before using the report.
What does the inequality margin mean?
It shows how far the sides are from breaking triangle inequality. A small margin means the triangle is nearly flat and may be sensitive to rounding.