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Solve non-right triangles with the law of sines and cosines. Enter three sides or a known combination of sides and angles, with a sketch.
Oblique triangle
1What data does the drawing give you?
2Enter the measurements
3Result
Click a dimension to copy it
Pythagoras alone cannot solve a drawing without a right angle. Enter three sides, two sides with their included angle, or one side and two angles to complete the triangle. The sketch identifies each angle and its opposite side.
Known measurements
Three sides: a = 60 mm · b = 50 mm · c = 40 mm
Result
A ≈ 82.819° · B ≈ 55.771° · C ≈ 41.410°
The angles total 180° before rounding. The largest angle is opposite the 60 mm side.
For three sides, the longest must be shorter than the sum of the other two. For two sides and an angle, enter the angle between those sides, not an exterior angle. Two supplied angles must be positive and add up to less than 180°.
The law of sines, a/sin A = b/sin B = c/sin C, pairs each side with its opposite angle. Two sides and their included angle use the law of cosines: c² = a² + b² − 2ab cos C. Match the drawing to the sketch to avoid using the wrong side-angle pair.
Two sides and an angle that is not included between them can produce two solutions. This calculator does not accept that ambiguous input case. Find another dimension or establish which arrangement represents the actual part first.
They determine the shape but you still need one side to establish the triangle's size.
All sides must be positive and the longest must be shorter than the sum of the other two. Equality produces a flat, degenerate triangle.
It is the angle at the vertex where the two known sides meet. The third side is opposite that angle.
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