Triangle calculator

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

Acute scalene triangle.

Sides: a = 956.2187782649   b = 857.3211409974   c = 700

Area: T = 289838.1121964
Perimeter: p = 2513.539919262
Semiperimeter: s = 1256.776959631

Angle ∠ A = α = 75° = 1.3098996939 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 606.2187782649
Height: hb = 676.1488078402
Height: hc = 828.1098891325

Median: ma = 619.6066236279
Median: mb = 720.018821083
Median: mc = 837.965955984

Inradius: r = 230.6221517909
Circumradius: R = 494.9754746831

Vertex coordinates: A[700; 0] B[0; 0] C[478.1098891325; 828.1098891325]
Centroid: CG[392.7032963775; 276.0366297108]
Coordinates of the circumscribed circle: U[350; 350]
Coordinates of the inscribed circle: I[399.4488186337; 230.6221517909]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105° = 1.3098996939 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 135° = 0.78553981634 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     