Triangle calculator ASA

Please enter the side of the triangle and two adjacent angles
°
°

Acute scalene triangle.

Sides: a = 20.06106404638   b = 21.31768537518   c = 12.5

Area: T = 122.6399170868
Perimeter: p = 53.87774942156
Semiperimeter: s = 26.93987471078

Angle ∠ A = α = 67° = 1.16993705988 rad
Angle ∠ B = β = 78° = 1.36113568166 rad
Angle ∠ C = γ = 35° = 0.61108652382 rad

Height: ha = 12.22768450092
Height: hb = 11.50663106682
Height: hc = 19.62222673389

Median: ma = 14.30881027038
Median: mb = 12.87439110002
Median: mc = 19.73221127821

Inradius: r = 4.5532519476
Circumradius: R = 10.89765424726

Vertex coordinates: A[12.5; 0] B[0; 0] C[4.17108416777; 19.62222673389]
Centroid: CG[5.55769472259; 6.54107557796]
Coordinates of the circumscribed circle: U[6.25; 8.92659250421]
Coordinates of the inscribed circle: I[5.6221893356; 4.5532519476]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 113° = 1.16993705988 rad
∠ B' = β' = 102° = 1.36113568166 rad
∠ C' = γ' = 145° = 0.61108652382 rad

How did we calculate this triangle?

1. Calculate the third unknown inner angle 2. By using the law of sines, we calculate unknown side a 3. By using the law of sines, we calculate last unknown side b Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     