Triangle Inequality Theorem Calculator
The triangle inequality theorem calculator is here to check whether the three line segments can make up a triangle or not.
Can these form a triangle?Noat least one inequality fails
Longest side12
Sum of the other two9
Third side must be between1 and 9given sides a and b, exclusive at both ends
The three tests
| Test | Comparison | Result |
|---|---|---|
| a + b > c | 9 vs 12 | fails |
| a + c > b | 16 vs 5 | passes |
| b + c > a | 17 vs 4 | passes |
The formula
a + b > c must hold for all three pairings
What always holds
- The three angles add to 180°, without exception.
- Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
- The longest side always faces the largest angle.
Area = ½ × base × heightfor any triangle, with the height measured perpendicular to that base.
Which formula to reach for
With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.