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 = 33   b = 16.5   c = 28.57988383249

Area: T = 235.775541618
Perimeter: p = 78.07988383249
Semiperimeter: s = 39.03994191624

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 14.28994191624
Height: hb = 28.57988383249
Height: hc = 16.5

Median: ma = 16.5
Median: mb = 29.74657980226
Median: mc = 21.82774483163

Inradius: r = 6.03994191624
Circumradius: R = 16.5

Vertex coordinates: A[28.57988383249; 0] B[0; 0] C[28.57988383249; 16.5]
Centroid: CG[19.05325588833; 5.5]
Coordinates of the circumscribed circle: U[14.28994191624; 8.25]
Coordinates of the inscribed circle: I[22.53994191624; 6.03994191624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 120° = 1.04771975512 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     