Triangle calculator

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

Right scalene triangle.

Sides: a = 8.66602540378   b = 7.5   c = 4.33301270189

Area: T = 16.2387976321
Perimeter: p = 20.49903810568
Semiperimeter: s = 10.24551905284

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

Height: ha = 3.75
Height: hb = 4.33301270189
Height: hc = 7.5

Median: ma = 4.33301270189
Median: mb = 5.72882196187
Median: mc = 7.8066247498

Inradius: r = 1.58549364905
Circumradius: R = 4.33301270189

Vertex coordinates: A[4.33301270189; 0] B[0; 0] C[4.33301270189; 7.5]
Centroid: CG[2.88767513459; 2.5]
Coordinates of the circumscribed circle: U[2.16550635095; 3.75]
Coordinates of the inscribed circle: I[2.74551905284; 1.58549364905]

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

How did we calculate this triangle?

1. Input data entered: side b, angle β and angle γ. 2. From angle γ, angle β and side b we calculate side c - By using the law of sines, we calculate unknown side c: 3. Calculation of the third side a 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. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     