Obtuse Triangle Calculator
Check if three angles form a valid obtuse triangle. Enter angles A, B, C to verify the 180 deg sum rule and identify triangles with an angle over 90 degrees.
About This Calculator
The Obtuse Triangle Calculator determines whether three given angles can form a valid triangle and whether that triangle is obtuse. In Euclidean geometry, the three interior angles of any valid triangle must sum to exactly 180 degrees. An obtuse triangle is defined as having one angle that exceeds 90 degrees while the other two remain acute (less than 90 degrees).
How to identify an obtuse triangle: Enter any three angle values (in degrees) into the calculator. The tool checks two conditions: first, whether the angles sum to 180 deg within a small floating-point tolerance; second, whether any individual angle is greater than 90 deg. If both are true, the triangle is classified as obtuse. If the sum equals 180 deg but all angles are less than 90 deg, the triangle is acute. If one angle equals exactly 90 deg, the triangle is right, not obtuse.
Triangle classification by angles: Acute (all angles < 90 deg), Right (one angle = 90 deg), Obtuse (one angle > 90 deg), and Invalid (angles do not sum to 180 deg or any angle is zero or negative). The calculator returns all three classifications so you can instantly understand your angle set.
Applications: Obtuse triangle identification is fundamental in geometry education, surveying, architecture, and engineering. Students use it to practice triangle classification, teachers use it to verify homework problems, and professionals use it when analyzing land plots, roof pitches, or structural loads involving oblique triangles.
Regional notes: Angle measurement in degrees is universal. The obtuse triangle definition (one angle > 90 deg) applies equivalently in all countries and educational systems including IN, US, and UK curricula. No regional conversion is needed for this purely geometric tool.
Frequently Asked Questions
What is an obtuse triangle?
An obtuse triangle is a triangle that has one angle measuring greater than 90 degrees and less than 180 degrees. The other two angles are acute (less than 90 degrees). The sum of all three interior angles still equals exactly 180 degrees, as with any Euclidean triangle.
How do I know if my triangle is obtuse?
Enter all three angles into the calculator. If the angles sum to 180 deg (within tolerance) and any single angle exceeds 90 deg, the triangle is classified as obtuse. If all angles are under 90 deg, it is acute. If exactly 90 deg, it is a right triangle.
Can an obtuse triangle be valid?
Yes, an obtuse triangle is a perfectly valid triangle. The only requirement is that all three interior angles sum to exactly 180 degrees. As long as one angle is between 90 deg and 180 deg and the other two are positive acute angles that complete the 180 deg total, the triangle is geometrically valid.
Can an obtuse triangle be isosceles or equilateral?
An obtuse triangle can be isosceles but never equilateral. An isosceles obtuse triangle has two equal acute angles and one obtuse angle. An equilateral triangle has all three angles equal to 60 deg, so none can exceed 90 deg.
What are the properties of an obtuse triangle?
An obtuse triangle has one angle between 90 deg and 180 deg, two acute angles less than 90 deg, the circumcenter lies outside the triangle, the longest side is opposite the obtuse angle, and the triangle is always scalene or isosceles. Obtuse triangles are one of the two types of oblique triangles (the other being acute triangles).
Can any set of three angles form an obtuse triangle?
No. Three angles can form a triangle only if they sum to exactly 180 deg. For the triangle to be obtuse, exactly one of those angles must be greater than 90 deg. If the sum is not 180 deg, the angles do not represent a valid Euclidean triangle.