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 = 146.358758202   b = 110   c = 178.4254756503

Area: T = 8038.635522225
Perimeter: p = 434.7822338523
Semiperimeter: s = 217.3911169262

Angle ∠ A = α = 55° = 0.96599310886 rad
Angle ∠ B = β = 38° = 0.66332251158 rad
Angle ∠ C = γ = 87° = 1.51884364492 rad

Height: ha = 109.8499248823
Height: hb = 146.1577004041
Height: hc = 90.10767248718

Median: ma = 128.8989725784
Median: mb = 153.6332573935
Median: mc = 93.8165896703

Inradius: r = 36.97877450002
Circumradius: R = 89.33548085016

Vertex coordinates: A[178.4254756503; 0] B[0; 0] C[115.3311348504; 90.10767248718]
Centroid: CG[97.91987016689; 30.03655749573]
Coordinates of the circumscribed circle: U[89.21223782513; 4.67554226287]
Coordinates of the inscribed circle: I[107.3911169261; 36.97877450002]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125° = 0.96599310886 rad
∠ B' = β' = 142° = 0.66332251158 rad
∠ C' = γ' = 93° = 1.51884364492 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     