Triangle calculator

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

Acute scalene triangle.

Sides: a = 7.9   b = 8.71223093636   c = 5.8

Area: T = 22.35495550283
Perimeter: p = 22.41223093636
Semiperimeter: s = 11.20661546818

Angle ∠ A = α = 62.2° = 62°12' = 1.08655947947 rad
Angle ∠ B = β = 77.30106669355° = 77°18'2″ = 1.3499151152 rad
Angle ∠ C = γ = 40.49993330645° = 40°29'58″ = 0.70768467068 rad

Height: ha = 5.6588115197
Height: hb = 5.13105696562
Height: hc = 7.70767431132

Median: ma = 6.25985675057
Median: mb = 5.39897046662
Median: mc = 7.79440469092

Inradius: r = 1.99444000117
Circumradius: R = 4.46553910842

Vertex coordinates: A[5.8; 0] B[0; 0] C[1.73766953063; 7.70767431132]
Centroid: CG[2.51222317688; 2.56989143711]
Coordinates of the circumscribed circle: U[2.9; 3.3965543776]
Coordinates of the inscribed circle: I[2.49438453182; 1.99444000117]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.8° = 117°48' = 1.08655947947 rad
∠ B' = β' = 102.6999333065° = 102°41'58″ = 1.3499151152 rad
∠ C' = γ' = 139.5010666935° = 139°30'2″ = 0.70768467068 rad

How did we calculate this triangle?

1. Input data entered: side a, c and angle α. 2. From angle α, side c and side a we calculate side b - by using the law of cosines and quadratic equation:  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     