Triangle calculator

Please enter what you know about the triangle:
You have entered height ha, height hb and height hc.

Equilateral triangle.

Sides: a = 3.46441016151   b = 3.46441016151   c = 3.46441016151

Area: T = 5.19661524227
Perimeter: p = 10.39223048454
Semiperimeter: s = 5.19661524227

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

Height: ha = 3
Height: hb = 3
Height: hc = 3

Median: ma = 3
Median: mb = 3
Median: mc = 3

Inradius: r = 1
Circumradius: R = 2

Vertex coordinates: A[3.46441016151; 0] B[0; 0] C[1.73220508076; 3]
Centroid: CG[1.73220508076; 1]
Coordinates of the circumscribed circle: U[1.73220508076; 1]
Coordinates of the inscribed circle: I[1.73220508076; 1]

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: height ha, height hb and height hc. 2. From height ha, height hb and height hc we calculate area T:  3. From area T and height ha we calculate side a: 4. From area T and height hb we calculate side b: 5. From area T and height hc we calculate 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. 6. The triangle circumference is the sum of the lengths of its three sides 7. Semiperimeter of the triangle 8. The triangle area using Heron's formula 9. Calculate the heights of the triangle from its area. 10. Calculation of the inner angles of the triangle using a Law of Cosines     