Obtuse Triangle Calculator
Solve obtuse triangles (one angle greater than 90°) using the law of cosines and law of sines. Find sides, angles, area and perimeter from any 3 inputs.
An obtuse triangle has one angle greater than 90 degrees and two acute angles (less than 90°). The triangle calculator on this site solves obtuse triangles the same way it handles right and acute ones, using the law of sines and the law of cosines.
What Makes a Triangle Obtuse
The three angles of any triangle sum to 180°. If one angle exceeds 90°, the other two must together make less than 90°. So an obtuse triangle always has exactly one obtuse angle and two acute ones. There is no such thing as an obtuse-right or two-obtuse triangle.
Example Obtuse Triangle
Sides a=4, b=5, c=8. Check: 4² + 5² = 16 + 25 = 41, while 8² = 64. Because c² > a² + b², the angle opposite c is obtuse. Plug these into the calculator and you get:
| Measurement | Value |
|---|---|
| Angle A (opposite side 4) | ≈ 24.15° |
| Angle B (opposite side 5) | ≈ 30.75° |
| Angle C (opposite side 8) | ≈ 125.10° (obtuse) |
| Area | ≈ 8.18 (Heron's formula) |
| Perimeter | 17 |
The Math: Law of Cosines
For an obtuse triangle, the law of cosines gives the angle opposite the longest side a negative cosine value, which translates to an angle above 90°.
Formula: cos(C) = (a² + b² − c²) / (2ab)
If c is the longest side and c² > a² + b², the numerator is negative, so cos(C) is negative, and C is in the obtuse range (90°-180°).
How to Identify an Obtuse Triangle Quickly
- Identify the longest side. Call it c.
- Compute a² + b² for the other two sides.
- Compare to c². If c² is larger, the triangle is obtuse. If equal, right. If smaller, acute.
Use the Full Calculator
The Triangle Calculator handles every scenario described on this page. For the deeper math and worked examples, read the companion guide.