Triangle calculator

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

Right scalene triangle.

Sides: a = 60   b = 34.64110161514   c = 69.28220323028

Area: T = 1039.233048454
Perimeter: p = 163.9233048454
Semiperimeter: s = 81.96215242271

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 34.64110161514
Height: hb = 60
Height: hc = 30

Median: ma = 45.82657569496
Median: mb = 62.4549979984
Median: mc = 34.64110161514

Inradius: r = 12.67994919243
Circumradius: R = 34.64110161514

Vertex coordinates: A[69.28220323028; 0] B[0; 0] C[51.96215242271; 30]
Centroid: CG[40.41545188433; 10]
Coordinates of the circumscribed circle: U[34.64110161514; -0]
Coordinates of the inscribed circle: I[47.32105080757; 12.67994919243]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 90° = 1.57107963268 rad

How did we calculate this triangle?

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