Triangle calculator

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

Acute scalene triangle.

Sides: a = 481.8222115079   b = 383.4122350648   c = 350

Area: T = 66444.17664013
Perimeter: p = 1215.234446573
Semiperimeter: s = 607.6177232863

Angle ∠ A = α = 82° = 1.43111699866 rad
Angle ∠ B = β = 52° = 0.9087571211 rad
Angle ∠ C = γ = 46° = 0.80328514559 rad

Height: ha = 275.8043763762
Height: hb = 346.594382406
Height: hc = 379.6811008008

Median: ma = 276.9743604645
Median: mb = 374.933335092
Median: mc = 398.6990093436

Inradius: r = 109.3522027572
Circumradius: R = 243.2798628428

Vertex coordinates: A[350; 0] B[0; 0] C[296.6399314214; 379.6811008008]
Centroid: CG[215.5466438071; 126.5660336003]
Coordinates of the circumscribed circle: U[175; 168.9965535591]
Coordinates of the inscribed circle: I[224.2054882215; 109.3522027572]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98° = 1.43111699866 rad
∠ B' = β' = 128° = 0.9087571211 rad
∠ C' = γ' = 134° = 0.80328514559 rad

How did we calculate this triangle?

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