Triangle calculator

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

Acute scalene triangle.

Sides: a = 21.99111485751   b = 28.27112756537   c = 21.99111485751

Area: T = 238.1321741867
Perimeter: p = 72.2543572804
Semiperimeter: s = 36.1276786402

Angle ∠ A = α = 50° = 0.8732664626 rad
Angle ∠ B = β = 80° = 1.39662634016 rad
Angle ∠ C = γ = 50° = 0.8732664626 rad

Height: ha = 21.65770536144
Height: hb = 16.84661971638
Height: hc = 21.65770536144

Median: ma = 22.81552398072
Median: mb = 16.84661971638
Median: mc = 22.81552398072

Inradius: r = 6.59215561716
Circumradius: R = 14.35437028254

Vertex coordinates: A[21.99111485751; 0] B[0; 0] C[3.81987228749; 21.65770536144]
Centroid: CG[8.60332904833; 7.21990178715]
Coordinates of the circumscribed circle: U[10.99655742876; 9.22663823293]
Coordinates of the inscribed circle: I[7.85655107483; 6.59215561716]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130° = 0.8732664626 rad
∠ B' = β' = 100° = 1.39662634016 rad
∠ C' = γ' = 130° = 0.8732664626 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     