Triangle calculator

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

Obtuse isosceles triangle.

Sides: a = 51.38441739579   b = 51.38441739579   c = 89

Area: T = 1143.298787056
Perimeter: p = 191.7688347916
Semiperimeter: s = 95.88441739579

Angle ∠ A = α = 30° = 0.52435987756 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 120° = 2.09443951024 rad

Height: ha = 44.5
Height: hb = 44.5
Height: hc = 25.69220869789

Median: ma = 67.97548728085
Median: mb = 67.97548728085
Median: mc = 25.69220869789

Inradius: r = 11.92437390632
Circumradius: R = 51.38441739579

Vertex coordinates: A[89; 0] B[0; 0] C[44.5; 25.69220869789]
Centroid: CG[44.5; 8.5644028993]
Coordinates of the circumscribed circle: U[44.5; -25.69220869789]
Coordinates of the inscribed circle: I[44.5; 11.92437390632]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150° = 0.52435987756 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 60° = 2.09443951024 rad

How did we calculate this triangle?

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