Geometry Problem Solver Scalene triangle angles
A scalene triangle has three sides of different lengths, so its three angles are all different as well. They still add to 180°, like in every triangle. A scalene triangle can be acute, right or obtuse: the only thing ruled out is two angles being equal.
The angles still add to 180°
Being scalene changes nothing about the sum. Every triangle in flat geometry has angles totalling 180°, so if you know two angles you can always subtract to get the third: 180 - 58 - 34 = 88.
What scalene adds is a restriction on the shape of the answer: no two of the three may come out equal. If your working gives two identical angles, the triangle is isosceles and something upstream was wrong.
The largest angle faces the longest side
In any triangle the biggest angle sits opposite the biggest side, and the smallest opposite the smallest. In a scalene triangle this ordering is strict, because there are no ties anywhere.
That makes the ordering a useful check. If a problem hands you the three sides, you already know the order of the angles before computing a single one.
Scalene can still be right or obtuse
Scalene describes the sides; acute, right and obtuse describe the angles. The two labels are independent, so a triangle can be scalene and right at the same time, as the 3-4-5 triangle is.
The one combination that cannot exist is a scalene equiangular triangle, since equal angles force equal sides.
Triangles by their sides
| Name | Sides | Angles |
|---|---|---|
| Scalene | All three different | All three different |
| Isosceles | Two equal | Two equal |
| Equilateral | All three equal | All 60° |
Questions
Do scalene triangle angles add up to 180?
Yes. Every triangle adds to 180°, whatever its sides do. Scalene only means no two of the three angles are equal.
Can a scalene triangle have a right angle?
Yes. A right scalene triangle has one 90° angle and two different acute angles, such as 90°, 60° and 30°. The 3-4-5 triangle is the best known example.
Can a scalene triangle be equilateral?
No. Those are opposites: equilateral means all three sides equal, scalene means none are.
More geometry reference
Stuck on the actual problem
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