Triangle calculator

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

Right scalene triangle.

Sides: a = 1083.462158215   b = 417   c = 1000

Area: T = 208500
Perimeter: p = 2500.462158215
Semiperimeter: s = 1250.231079108

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 22.63661363795° = 22°38'10″ = 0.39550751098 rad
Angle ∠ C = γ = 67.36438636205° = 67°21'50″ = 1.1765721217 rad

Height: ha = 384.8787513766
Height: hb = 1000
Height: hc = 417

Median: ma = 541.7310791076
Median: mb = 1021.505489475
Median: mc = 651.0687584817

Inradius: r = 166.7699208924
Circumradius: R = 541.7310791076

Vertex coordinates: A[1000; 0] B[0; 0] C[1000; 417]
Centroid: CG[666.6676666667; 139]
Coordinates of the circumscribed circle: U[500; 208.5]
Coordinates of the inscribed circle: I[833.2310791076; 166.7699208924]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 157.3643863621° = 157°21'50″ = 0.39550751098 rad
∠ C' = γ' = 112.6366136379° = 112°38'10″ = 1.1765721217 rad

How did we calculate this triangle?

1. Input data entered: side b, c and angle α. 2. Calculation of the third side a 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     