Triangle calculator

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

Right scalene triangle.

Sides: a = 19.03992489729   b = 18.75   c = 3.30661308883

Area: T = 30.99549770777
Perimeter: p = 41.09553798611
Semiperimeter: s = 20.54876899306

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 80° = 1.39662634016 rad
Angle ∠ C = γ = 10° = 0.17545329252 rad

Height: ha = 3.25659033313
Height: hb = 3.30661308883
Height: hc = 18.75

Median: ma = 9.52196244864
Median: mb = 9.94108815731
Median: mc = 18.82327289563

Inradius: r = 1.50884409577
Circumradius: R = 9.52196244864

Vertex coordinates: A[3.30661308883; 0] B[0; 0] C[3.30661308883; 18.75]
Centroid: CG[2.20440872589; 6.25]
Coordinates of the circumscribed circle: U[1.65330654441; 9.375]
Coordinates of the inscribed circle: I[1.79876899306; 1.50884409577]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 100° = 1.39662634016 rad
∠ C' = γ' = 170° = 0.17545329252 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     