Triangle calculator

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

Right scalene triangle.

Sides: a = 4000   b = 6403.124423743   c = 5000

Area: T = 10000000
Perimeter: p = 15403.12442374
Semiperimeter: s = 7701.562211872

Angle ∠ A = α = 38.66598082541° = 38°39'35″ = 0.67547409422 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 51.34401917459° = 51°20'25″ = 0.89660553846 rad

Height: ha = 5000
Height: hb = 3123.475523777
Height: hc = 4000

Median: ma = 5385.165480713
Median: mb = 3201.562211872
Median: mc = 4716.991056603

Inradius: r = 1298.438788128
Circumradius: R = 3201.562211872

Vertex coordinates: A[5000; 0] B[0; 0] C[-0; 4000]
Centroid: CG[1666.667666667; 1333.333333333]
Coordinates of the circumscribed circle: U[2500; 2000]
Coordinates of the inscribed circle: I[1298.438788128; 1298.438788128]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.3440191746° = 141°20'25″ = 0.67547409422 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 128.6659808254° = 128°39'35″ = 0.89660553846 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     