Area of Oblique Triangle Calculator — Two Sides and Angle
Find the area of any oblique triangle — a triangle with no right angle — given two sides and the angle between them. The calculator also derives the third side, all three angles, and the perimeter using the law of cosines and law of sines.
°
Area = ½ × a × b × sin(C)
- 1
Angle in radians
60 × π ÷ 180 = 1.047198Convert the included angle C from degrees to radians for use in sin(). - 2
sin(C)
sin(1.047198) = 0.866025 - 3
Area
½ × 7 × 5 × 0.866025 = 15.1554
How does this calculator work?
Area of an oblique triangle = ½ × a × b × sin(C), where a and b are two sides and C is the angle between them. Works for any triangle — acute or obtuse. The law of cosines then gives the third side c² = a²+b²−2ab·cos(C), and the law of sines gives the remaining angles.
Formula
How this is calculated
An oblique triangle is any triangle without a 90° angle — all three angles are either all acute (less than 90°) or one is obtuse (greater than 90°). When two sides and their included angle (the SAS configuration) are known, the area formula is Area = ½ × a × b × sin(C), where C is the angle formed between sides a and b. This is derived from the standard base × height formula by noting that the height of the triangle equals b × sin(C).
Once the area is known, the third side c follows from the law of cosines: c² = a² + b² − 2ab·cos(C). The remaining angles A and B are then found with the law of sines: sin(A)/a = sin(C)/c, and B = 180° − A − C. Together these three tools fully solve the oblique triangle from the SAS input.
The formula degenerates to zero when C = 0° or C = 180° (the three vertices become collinear). For C = 90° the triangle is a right triangle and sin(90°) = 1, so the formula still works correctly — it simply reduces to the familiar ½ × a × b form for a right triangle with legs a and b.
Frequently asked questions
An oblique triangle is a triangle that has no right (90°) angle. It can be either acute (all angles less than 90°) or obtuse (one angle greater than 90°). Any triangle that is not a right triangle is oblique.
For three known sides, use Heron's formula: semi-perimeter s = (a+b+c)/2, Area = √[s(s−a)(s−b)(s−c)]. This calculator uses the SAS (two-sides-and-included-angle) method. To convert three sides to this form, first find an angle using the law of cosines: cos(C) = (a²+b²−c²)/(2ab).
You need the angle between (included by) the two known sides. If you have a different arrangement — such as two angles and one side — find the third angle first (angles sum to 180°), then use the law of sines to compute the missing side, then apply this formula.
Also known as
TG we-Calculate Editorial Team. (2026). Area of Oblique Triangle Calculator — Two Sides and Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/area-oblique-triangle-calculator
TG we-Calculate Editorial Team. "Area of Oblique Triangle Calculator — Two Sides and Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/area-oblique-triangle-calculator.
TG we-Calculate Editorial Team, "Area of Oblique Triangle Calculator — Two Sides and Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/area-oblique-triangle-calculator
@misc{wecalculate_area_oblique_triangle_calculator, title = {Area of Oblique Triangle Calculator — Two Sides and Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/area-oblique-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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