Obtuse Triangle Calculator
Calculate every property of an obtuse triangle — a triangle with one interior angle greater than 90°. Enter three sides (SSS) or two sides and the obtuse angle (SAS) to find all angles, area, perimeter, the three altitudes, inradius and circumradius.
Known elements
Area of the obtuse triangle
- 1
Angle C
111.804° - 2
sin C
sin(111.804°) = 0.9285 - 3
½ × a × b
½ × 5 × 7 = 17.5 - 4
Area = ½ · a · b · sin C
17.5 × 0.9285 = 16.2481
How does this calculator work?
An obtuse triangle has one angle > 90°. Use the law of cosines to solve from SSS (cos C = (a²+b²−c²)/(2ab)) or SAS (c² = a²+b²−2ab cos C). Area = ½ab sin C; altitudes h_a = 2A/a; inradius r = A/s; circumradius R = abc/(4A). The circumcentre and two altitudes lie outside the triangle.
Formula
How this is calculated
An obtuse triangle has exactly one interior angle greater than 90° (and therefore the other two must each be less than 90°). Any triangle that is not a right triangle and not equilateral or equiangular falls into either the acute (all angles < 90°) or obtuse category. The obtuse angle is always opposite the longest side.
For SSS input the calculator uses the law of cosines to find each angle in turn: cos C = (a² + b² − c²)/(2ab). The largest angle is checked to confirm it exceeds 90°. For SAS (two sides and the included obtuse angle) the third side is found with the law of cosines and the remaining angles with further applications of the same law.
A distinctive geometric property of obtuse triangles is that two of the three altitudes (heights from a vertex perpendicular to the opposite side) fall outside the triangle — they must be extended to a line containing the side rather than the side itself. The altitudes are computed as h_a = 2·Area/a, h_b = 2·Area/b, h_c = 2·Area/c. The inradius r = Area/s (s = semi-perimeter) and circumradius R = abc/(4·Area) apply to any triangle; for obtuse triangles the circumcentre lies outside the triangle.
Frequently asked questions
A triangle is obtuse if c² > a² + b², where c is the longest side. Equivalently, compute the cosine of the largest angle using the law of cosines — if it is negative the angle is greater than 90° and the triangle is obtuse.
The circumcentre (centre of the circumscribed circle) lies outside the triangle for an obtuse triangle, on the opposite side of the longest side from the obtuse angle vertex. This contrasts with acute triangles where the circumcentre is inside.
Yes. An isosceles obtuse triangle has two equal sides and one angle greater than 90°. For example, sides 5, 5, 8 form a valid obtuse isosceles triangle with the obtuse angle opposite the longest side (8).
Also known as
TG we-Calculate Editorial Team. (2026). Obtuse Triangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/obtuse-triangle-calculator
TG we-Calculate Editorial Team. "Obtuse Triangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/obtuse-triangle-calculator.
TG we-Calculate Editorial Team, "Obtuse Triangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/obtuse-triangle-calculator
@misc{wecalculate_obtuse_triangle_calculator, title = {Obtuse Triangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/obtuse-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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