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 = 1000   b = 17.45550649282   c = 1000.152232804

Area: T = 8727.532246411
Perimeter: p = 2017.607739297
Semiperimeter: s = 1008.804369649

Angle ∠ A = α = 89° = 1.55333430343 rad
Angle ∠ B = β = 1° = 0.01774532925 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 17.45550649282
Height: hb = 1000
Height: hc = 17.45224064373

Median: ma = 500.3054586519
Median: mb = 1000.038808419
Median: mc = 500.0766164022

Inradius: r = 8.65113684422
Circumradius: R = 500.0766164022

Vertex coordinates: A[1000.152232804; 0] B[0; 0] C[999.8487695156; 17.45224064373]
Centroid: CG[666.66766744; 5.81774688124]
Coordinates of the circumscribed circle: U[500.0766164022; -0]
Coordinates of the inscribed circle: I[991.3498631558; 8.65113684422]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 91° = 1.55333430343 rad
∠ B' = β' = 179° = 0.01774532925 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     