Triangle calculator ASA

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

Acute scalene triangle.

Sides: a = 11.08223604879   b = 12.9410902488   c = 8.4

Area: T = 46.09329324134
Perimeter: p = 32.42332629759
Semiperimeter: s = 16.21216314879

Angle ∠ A = α = 58° = 1.01222909662 rad
Angle ∠ B = β = 82° = 1.43111699866 rad
Angle ∠ C = γ = 40° = 0.69881317008 rad

Height: ha = 8.31882517774
Height: hb = 7.12436040077
Height: hc = 10.97545077175

Median: ma = 9.39772762067
Median: mb = 7.40442297163
Median: mc = 11.29217153521

Inradius: r = 2.84332013427
Circumradius: R = 6.53440400728

Vertex coordinates: A[8.4; 0] B[0; 0] C[1.54223664751; 10.97545077175]
Centroid: CG[3.31441221584; 3.65881692392]
Coordinates of the circumscribed circle: U[4.2; 5.00553650889]
Coordinates of the inscribed circle: I[3.2710729; 2.84332013427]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122° = 1.01222909662 rad
∠ B' = β' = 98° = 1.43111699866 rad
∠ C' = γ' = 140° = 0.69881317008 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     