Triangle calculator

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

Right scalene triangle.

Sides: a = 2000   b = 174.9777327052   c = 2007.643967509

Area: T = 174977.3277052
Perimeter: p = 4182.617700214
Semiperimeter: s = 2091.309850107

Angle ∠ A = α = 85° = 1.48435298642 rad
Angle ∠ B = β = 5° = 0.08772664626 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 174.9777327052
Height: hb = 2000
Height: hc = 174.3111485495

Median: ma = 1015.193311709
Median: mb = 2001.9132652
Median: mc = 1003.821983754

Inradius: r = 83.66988259826
Circumradius: R = 1003.821983754

Vertex coordinates: A[2007.643967509; 0] B[0; 0] C[1992.389939618; 174.3111485495]
Centroid: CG[1333.343302376; 58.10438284984]
Coordinates of the circumscribed circle: U[1003.821983754; 0]
Coordinates of the inscribed circle: I[1916.331117402; 83.66988259826]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 95° = 1.48435298642 rad
∠ B' = β' = 175° = 0.08772664626 rad
∠ C' = γ' = 90° = 1.57107963268 rad

How did we calculate this triangle?

1. Input data entered: side a, angle β and angle γ. 2. From angle β and angle γ we calculate angle α: 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     