Triangle calculator

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

Right scalene triangle.

Sides: a = 100   b = 93.96992620786   c = 34.20220143326

Area: T = 1606.969902422
Perimeter: p = 228.1711276411
Semiperimeter: s = 114.0865638206

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 70° = 1.22217304764 rad
Angle ∠ C = γ = 20° = 0.34990658504 rad

Height: ha = 32.13993804843
Height: hb = 34.20220143326
Height: hc = 93.96992620786

Median: ma = 50
Median: mb = 58.1154828902
Median: mc = 95.5132651841

Inradius: r = 14.08656382056
Circumradius: R = 50

Vertex coordinates: A[34.20220143326; 0] B[0; 0] C[34.20220143326; 93.96992620786]
Centroid: CG[22.80113428884; 31.32330873595]
Coordinates of the circumscribed circle: U[17.10110071663; 46.98546310393]
Coordinates of the inscribed circle: I[20.1166376127; 14.08656382056]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 110° = 1.22217304764 rad
∠ C' = γ' = 160° = 0.34990658504 rad

How did we calculate this triangle?

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