Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 10.2   b = 15.55334998432   c = 7.79656230659

Area: T = 34.77328483704
Perimeter: p = 33.5499122909
Semiperimeter: s = 16.77545614545

Angle ∠ A = α = 35° = 0.61108652382 rad
Angle ∠ B = β = 119° = 2.07769418099 rad
Angle ∠ C = γ = 26° = 0.45437856055 rad

Height: ha = 6.81882055628
Height: hb = 4.47113856972
Height: hc = 8.92111210128

Median: ma = 11.19551573539
Median: mb = 4.68327374632
Median: mc = 12.56111601351

Inradius: r = 2.0732951264
Circumradius: R = 8.89215786577

Vertex coordinates: A[7.79656230659; 0] B[0; 0] C[-4.94550581265; 8.92111210128]
Centroid: CG[0.95501883131; 2.97437070043]
Coordinates of the circumscribed circle: U[3.89878115329; 7.99216979597]
Coordinates of the inscribed circle: I[1.22110616114; 2.0732951264]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145° = 0.61108652382 rad
∠ B' = β' = 61° = 2.07769418099 rad
∠ C' = γ' = 154° = 0.45437856055 rad

How did we calculate this triangle?

1. Input data entered: side a, angle α and angle γ. 2. From angle α and angle γ we calculate angle β: 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     