Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 4.18439772164   b = 5.7   c = 8.26990237854

Area: T = 11.00333285735
Perimeter: p = 18.15330010017
Semiperimeter: s = 9.07765005009

Angle ∠ A = α = 27.83333333333° = 27°50' = 0.48657833085 rad
Angle ∠ B = β = 39.5° = 39°30' = 0.68994050545 rad
Angle ∠ C = γ = 112.6676666667° = 112°40' = 1.96664042906 rad

Height: ha = 5.26597459328
Height: hb = 3.86108170433
Height: hc = 2.66113367815

Median: ma = 6.78765278932
Median: mb = 5.90107380771
Median: mc = 2.8111342043

Inradius: r = 1.21222875521
Circumradius: R = 4.48105810184

Vertex coordinates: A[8.26990237854; 0] B[0; 0] C[3.22884596765; 2.66113367815]
Centroid: CG[3.83224944873; 0.88771122605]
Coordinates of the circumscribed circle: U[4.13545118927; -1.7276678219]
Coordinates of the inscribed circle: I[3.37765005009; 1.21222875521]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.1676666667° = 152°10' = 0.48657833085 rad
∠ B' = β' = 140.5° = 140°30' = 0.68994050545 rad
∠ C' = γ' = 67.33333333333° = 67°20' = 1.96664042906 rad

How did we calculate this triangle?

1. Input data entered: side b, angle α and angle β. 2. From angle α and angle β we calculate angle γ: 3. From angle α, angle β and side b we calculate side a - By using the law of sines, we calculate unknown side a: 4. Calculation of the third side c of the triangle using a Law of Cosines 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     