Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 4.6   b = 1.49985263723   c = 4.29770876316

Area: T = 3.21876882464
Perimeter: p = 10.39656140038
Semiperimeter: s = 5.19878070019

Angle ∠ A = α = 92° = 1.60657029118 rad
Angle ∠ B = β = 19° = 0.33216125579 rad
Angle ∠ C = γ = 69° = 1.20442771839 rad

Height: ha = 1.39989948898
Height: hb = 4.29444699619
Height: hc = 1.49876135105

Median: ma = 2.25106158493
Median: mb = 4.38876059229
Median: mc = 2.66220574967

Inradius: r = 0.61990472723
Circumradius: R = 2.30114019519

Vertex coordinates: A[4.29770876316; 0] B[0; 0] C[4.34993854478; 1.49876135105]
Centroid: CG[2.88221576931; 0.49992045035]
Coordinates of the circumscribed circle: U[2.14985438158; 0.82547486986]
Coordinates of the inscribed circle: I[3.69992806296; 0.61990472723]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 88° = 1.60657029118 rad
∠ B' = β' = 161° = 0.33216125579 rad
∠ C' = γ' = 111° = 1.20442771839 rad

How did we calculate this triangle?

1. Input data entered: side a, angle α and angle β. 2. From angle α and angle β we calculate angle γ: 3. From angle β, angle α and side a we calculate side b - By using the law of sines, we calculate unknown side b: 4. From angle γ, angle α and side a we calculate side c - By using the law of sines, we calculate unknown side c: 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. 5. The triangle circumference is the sum of the lengths of its three sides 6. Semiperimeter of the triangle 7. The triangle area using Heron's formula 8. Calculate the heights of the triangle from its area. 9. Calculation of the inner angles of the triangle using a Law of Cosines     