Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 50   b = 50.80329652905   c = 90

Area: T = 1021.479862441
Perimeter: p = 190.803296529
Semiperimeter: s = 95.40114826452

Angle ∠ A = α = 26.54395180817° = 26°32'22″ = 0.46332019724 rad
Angle ∠ B = β = 27° = 0.4711238898 rad
Angle ∠ C = γ = 126.4660481918° = 126°27'38″ = 2.20771517831 rad

Height: ha = 40.85991449766
Height: hb = 40.21333465467
Height: hc = 22.7699524987

Median: ma = 68.6699284554
Median: mb = 68.22658358646
Median: mc = 22.70439785314

Inradius: r = 10.70771567033
Circumradius: R = 55.95215731272

Vertex coordinates: A[90; 0] B[0; 0] C[44.55503262094; 22.7699524987]
Centroid: CG[44.85501087365; 7.5676508329]
Coordinates of the circumscribed circle: U[45; -33.25502411331]
Coordinates of the inscribed circle: I[44.59985173548; 10.70771567033]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4660481918° = 153°27'38″ = 0.46332019724 rad
∠ B' = β' = 153° = 0.4711238898 rad
∠ C' = γ' = 53.54395180817° = 53°32'22″ = 2.20771517831 rad

How did we calculate this triangle?

1. Input data entered: side a, c and angle β. 2. 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. 3. The triangle circumference is the sum of the lengths of its three sides 4. Semiperimeter of the triangle 5. The triangle area using Heron's formula 6. Calculate the heights of the triangle from its area. 7. Calculation of the inner angles of the triangle using a Law of Cosines     