Triangle calculator ASA

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Acute scalene triangle.

Sides: a = 688.3177307256   b = 547.7321929497   c = 500

Area: T = 135600.3660003
Perimeter: p = 1736.049923675
Semiperimeter: s = 868.0254618376

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

Height: ha = 394.0055376803
Height: hb = 495.1344034371
Height: hc = 542.4011440011

Median: ma = 395.6776578064
Median: mb = 535.6199072743
Median: mc = 569.5577276337

Vertex coordinates: A[500; 0] B[0; 0] C[423.7770448877; 542.4011440011]
Centroid: CG[307.9233482959; 180.8800480004]
Coordinates of the circumscribed circle: U[250; 241.4222193702]
Coordinates of the inscribed circle: I[320.2932688879; 156.2177182246]

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. Calculate the third unknown inner angle 2. By using the law of sines, we calculate unknown side a 3. By using the law of sines, we calculate last unknown side b 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    