Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 16.24659848116   b = 42.53325404176   c = 50

Area: T = 328.5821945075
Perimeter: p = 108.7798525229
Semiperimeter: s = 54.38992626146

Angle ∠ A = α = 18° = 0.31441592654 rad
Angle ∠ B = β = 54° = 0.94224777961 rad
Angle ∠ C = γ = 108° = 1.88549555922 rad

Height: ha = 40.45108497187
Height: hb = 15.45108497187
Height: hc = 13.1433277803

Median: ma = 45.77003883087
Median: mb = 30.49111751603
Median: mc = 20.28548344444

Inradius: r = 6.0411301707
Circumradius: R = 26.2876555606

Vertex coordinates: A[50; 0] B[0; 0] C[9.54991502813; 13.1433277803]
Centroid: CG[19.85497167604; 4.3811092601]
Coordinates of the circumscribed circle: U[25; -8.12329924058]
Coordinates of the inscribed circle: I[11.8576722197; 6.0411301707]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162° = 0.31441592654 rad
∠ B' = β' = 126° = 0.94224777961 rad
∠ C' = γ' = 72° = 1.88549555922 rad

How did we calculate this triangle?

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