Triangle calculator

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

Right scalene triangle.

Sides: a = 1003.461090197   b = 83.26993327934   c = 1000

Area: T = 41634.66663967
Perimeter: p = 2086.733023476
Semiperimeter: s = 1043.365511738

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 4.76° = 4°45'36″ = 0.08330776724 rad
Angle ∠ C = γ = 85.24° = 85°14'24″ = 1.48877186544 rad

Height: ha = 82.98221397424
Height: hb = 1000
Height: hc = 83.26993327934

Median: ma = 501.7330450985
Median: mb = 1000.866634744
Median: mc = 506.8866359832

Inradius: r = 39.90442154113
Circumradius: R = 501.7330450985

Vertex coordinates: A[1000; 0] B[0; 0] C[1000; 83.26993327934]
Centroid: CG[666.6676666667; 27.75664442645]
Coordinates of the circumscribed circle: U[500; 41.63546663967]
Coordinates of the inscribed circle: I[960.0965784589; 39.90442154113]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 175.24° = 175°14'24″ = 0.08330776724 rad
∠ C' = γ' = 94.76° = 94°45'36″ = 1.48877186544 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     