Triangle calculator

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

Acute scalene triangle.

Sides: a = 80.18766663967   b = 68   c = 96.68546582675

Area: T = 2692.781080602
Perimeter: p = 244.8711324664
Semiperimeter: s = 122.4365662332

Angle ∠ A = α = 55° = 0.96599310886 rad
Angle ∠ B = β = 44° = 0.76879448709 rad
Angle ∠ C = γ = 81° = 1.41437166941 rad

Height: ha = 67.16328071605
Height: hb = 79.19994354712
Height: hc = 55.70223390117

Median: ma = 73.33881633612
Median: mb = 82.05443253342
Median: mc = 56.4879818943

Inradius: r = 21.99334352029
Circumradius: R = 48.94549223473

Vertex coordinates: A[96.68546582675; 0] B[0; 0] C[57.68114605956; 55.70223390117]
Centroid: CG[51.45553729544; 18.56774463372]
Coordinates of the circumscribed circle: U[48.34223291337; 7.65766727438]
Coordinates of the inscribed circle: I[54.43656623321; 21.99334352029]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125° = 0.96599310886 rad
∠ B' = β' = 136° = 0.76879448709 rad
∠ C' = γ' = 99° = 1.41437166941 rad

How did we calculate this triangle?

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