Triangle calculator

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

Right scalene triangle.

Sides: a = 100   b = 40   c = 91.65215138991

Area: T = 1833.033027798
Perimeter: p = 231.6521513899
Semiperimeter: s = 115.826575695

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 23.57881784782° = 23°34'41″ = 0.41215168461 rad
Angle ∠ C = γ = 66.42218215218° = 66°25'19″ = 1.15992794807 rad

Height: ha = 36.66106055596
Height: hb = 91.65215138991
Height: hc = 40

Median: ma = 50
Median: mb = 93.80883151965
Median: mc = 60.8287625303

Inradius: r = 15.82657569496
Circumradius: R = 50

Vertex coordinates: A[91.65215138991; 0] B[0; 0] C[91.65215138991; 40]
Centroid: CG[61.10110092661; 13.33333333333]
Coordinates of the circumscribed circle: U[45.82657569496; 20]
Coordinates of the inscribed circle: I[75.82657569496; 15.82657569496]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 156.4221821522° = 156°25'19″ = 0.41215168461 rad
∠ C' = γ' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad

How did we calculate this triangle?

1. Input data entered: side a, b and angle α. 2. From angle α, side b and side a we calculate side c - 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     