Triangle calculator

Please enter what you know about the triangle:
You have entered height hc, angle α, angle β and angle γ.

Acute isosceles triangle.

Sides: a = 27.58444479741   b = 27.58444479741   c = 23.31553829077

Area: T = 291.4422286347
Perimeter: p = 78.48442788559
Semiperimeter: s = 39.24221394279

Angle ∠ A = α = 65° = 1.13444640138 rad
Angle ∠ B = β = 65° = 1.13444640138 rad
Angle ∠ C = γ = 50° = 0.8732664626 rad

Height: ha = 21.1310913087
Height: hb = 21.1310913087
Height: hc = 25

Median: ma = 21.49548594454
Median: mb = 21.49548594454
Median: mc = 25

Inradius: r = 7.42767685349
Circumradius: R = 15.21880354007

Vertex coordinates: A[23.31553829077; 0] B[0; 0] C[11.65876914539; 25]
Centroid: CG[11.65876914539; 8.33333333333]
Coordinates of the circumscribed circle: U[11.65876914539; 9.78219645993]
Coordinates of the inscribed circle: I[11.65876914539; 7.42767685349]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115° = 1.13444640138 rad
∠ B' = β' = 115° = 1.13444640138 rad
∠ C' = γ' = 130° = 0.8732664626 rad

How did we calculate this triangle?

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