Triangle calculator

Please enter what you know about the triangle:
You have entered side a, angle α and angle β.

Acute scalene triangle.

Sides: a = 50   b = 33.64108182402   c = 40.67436643076

Area: T = 680.4399841524
Perimeter: p = 124.3144482548
Semiperimeter: s = 62.15772412739

Angle ∠ A = α = 84° = 1.46660765717 rad
Angle ∠ B = β = 42° = 0.73330382858 rad
Angle ∠ C = γ = 54° = 0.94224777961 rad

Height: ha = 27.2165993661
Height: hb = 40.45108497187
Height: hc = 33.45765303179

Median: ma = 27.71332785869
Median: mb = 42.3598556646
Median: mc = 37.44768367674

Inradius: r = 10.94664292105
Circumradius: R = 25.13877069891

Vertex coordinates: A[40.67436643076; 0] B[0; 0] C[37.15772412739; 33.45765303179]
Centroid: CG[25.94436351938; 11.15221767726]
Coordinates of the circumscribed circle: U[20.33768321538; 14.77655734446]
Coordinates of the inscribed circle: I[28.51664230337; 10.94664292105]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 96° = 1.46660765717 rad
∠ B' = β' = 138° = 0.73330382858 rad
∠ C' = γ' = 126° = 0.94224777961 rad

How did we calculate this triangle?

1. Input data entered: side a, angle α and angle β. 2. From angle α and angle β we calculate angle γ: 3. From angle β, angle α and side a we calculate side b - By using the law of sines, we calculate unknown side b: 4. From angle γ, angle α and side a we calculate side c - By using the law of sines, we calculate unknown side c: 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. 5. The triangle circumference is the sum of the lengths of its three sides 6. Semiperimeter of the triangle 7. The triangle area using Heron's formula 8. Calculate the heights of the triangle from its area. 9. Calculation of the inner angles of the triangle using a Law of Cosines     