Triangle calculator

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

Acute scalene triangle.

Sides: a = 11.04218797561   b = 12.2   c = 11.99442573167

Area: T = 59.41660665835
Perimeter: p = 35.23661370728
Semiperimeter: s = 17.61880685364

Angle ∠ A = α = 54.3° = 54°18' = 0.94877137838 rad
Angle ∠ B = β = 63.8° = 63°48' = 1.11435200628 rad
Angle ∠ C = γ = 61.9° = 61°54' = 1.0880358807 rad

Height: ha = 10.76219477654
Height: hb = 9.74403387842
Height: hc = 9.90774190281

Median: ma = 10.76443080201
Median: mb = 9.78217513035
Median: mc = 9.97107573498

Inradius: r = 3.37224506441
Circumradius: R = 6.79884877112

Vertex coordinates: A[11.99442573167; 0] B[0; 0] C[4.87550545381; 9.90774190281]
Centroid: CG[5.62331039516; 3.30224730094]
Coordinates of the circumscribed circle: U[5.99771286583; 3.20221684863]
Coordinates of the inscribed circle: I[5.41880685364; 3.37224506441]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.7° = 125°42' = 0.94877137838 rad
∠ B' = β' = 116.2° = 116°12' = 1.11435200628 rad
∠ C' = γ' = 118.1° = 118°6' = 1.0880358807 rad

How did we calculate this triangle?

1. Input data entered: side b, angle α and angle β. 2. From angle α and angle β we calculate angle γ: 3. From angle α, angle β and side b we calculate side a - By using the law of sines, we calculate unknown side a: 4. Calculation of the third side c 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. 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     