You know some sides or angles of a triangle, from homework, a roof, a ramp or a map, and need the rest. You will label the triangle, choose which values you know, let the right rule do the work and check the answer. The calculator shows every step.
6-minute read
Today's result All three sides and angles, the area, the perimeter and the heights, with the working and a scaled drawing.
Use the same unit for every side, and degrees for angles. The area comes out in that unit squared.
Sketch the triangle and name its corners A, B and C. Side a is opposite corner A, side b opposite B and side c opposite C.
Each side is named after the angle opposite it; c is the hypotenuse of a right triangle.Open Triangle calculator
Right triangle? Tick it
If one angle is 90°, call it C and tick Right triangle (C = 90°). Then c is the hypotenuse and two values are enough: two sides use Pythagoras, a² + b² = c².
Enter three values
For any other triangle, enter three values with at least one side: three sides (SSS), two sides and the angle between them (SAS), or two angles and a side (ASA, AAS). Three angles alone fix the shape but not the size.
Let the rules work
With sides only or an angle between two sides, the law of cosines finds the missing piece: c² = a² + b² − 2ab · cos C. With a side and its opposite angle, the law of sines does: a / sin A = b / sin B = c / sin C.
Watch for two answers
Two sides and an angle that is not between them (SSA) can make two triangles, one acute and one obtuse. The calculator shows Triangle 1 and Triangle 2; pick the one that matches your sketch.
Two sides and a non-included angle can close in two places.
Read area and check
Area = ½ · b · c · sin A. Check that the angles add to 180° and that the longest side faces the largest angle. Copy result copies the values and the working.
