Triangle calculator

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

Acute isosceles triangle.

Sides: a = 17.32105080757   b = 17.32105080757   c = 17.32105080757

Area: T = 129.9043810568
Perimeter: p = 51.96215242271
Semiperimeter: s = 25.98107621135

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 15
Height: hb = 15
Height: hc = 15

Median: ma = 15
Median: mb = 15
Median: mc = 15

Inradius: r = 5
Circumradius: R = 10

Vertex coordinates: A[17.32105080757; 0] B[0; 0] C[8.66602540378; 15]
Centroid: CG[8.66602540378; 5]
Coordinates of the circumscribed circle: U[8.66602540378; 5]
Coordinates of the inscribed circle: I[8.66602540378; 5]

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

How did we calculate this triangle?

1. Input data entered: angle α, angle β and height hc. 2. From angle α and angle β we calculate angle γ: 3. 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. 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     