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 = 1.375   b = 1.73331495693   c = 1.05550746085

Area: T = 0.72553637933
Perimeter: p = 4.16332241777
Semiperimeter: s = 2.08216120889

Angle ∠ A = α = 52.5° = 52°30' = 0.91662978573 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 37.5° = 37°30' = 0.65444984695 rad

Height: ha = 1.05550746085
Height: hb = 0.83770469649
Height: hc = 1.375

Median: ma = 1.25993008693
Median: mb = 0.86765747846
Median: mc = 1.4732725571

Inradius: r = 0.34884625196
Circumradius: R = 0.86765747846

Vertex coordinates: A[1.05550746085; 0] B[0; 0] C[-0; 1.375]
Centroid: CG[0.35216915362; 0.45883333333]
Coordinates of the circumscribed circle: U[0.52875373042; 0.68875]
Coordinates of the inscribed circle: I[0.34884625196; 0.34884625196]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.5° = 127°30' = 0.91662978573 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 142.5° = 142°30' = 0.65444984695 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     