Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 58.05498098697   b = 16.82441275087   c = 61

Area: T = 488.0211230994
Perimeter: p = 135.8743937378
Semiperimeter: s = 67.93769686892

Angle ∠ A = α = 72° = 1.25766370614 rad
Angle ∠ B = β = 16° = 0.27992526803 rad
Angle ∠ C = γ = 92° = 1.60657029118 rad

Height: ha = 16.81438787048
Height: hb = 58.0144447494
Height: hc = 16.00106960982

Median: ma = 34.05326140955
Median: mb = 58.94659701451
Median: mc = 29.93660292319

Inradius: r = 7.18334413635
Circumradius: R = 30.51985911011

Vertex coordinates: A[61; 0] B[0; 0] C[55.80110586843; 16.00106960982]
Centroid: CG[38.93436862281; 5.33435653661]
Coordinates of the circumscribed circle: U[30.5; -1.06550834695]
Coordinates of the inscribed circle: I[51.11328411805; 7.18334413635]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108° = 1.25766370614 rad
∠ B' = β' = 164° = 0.27992526803 rad
∠ C' = γ' = 88° = 1.60657029118 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     