# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 6.69215220599   b = 5.0198641545   c = 4.0154913236

Area: T = 10.03772830899
Perimeter: p = 15.72550768409
Semiperimeter: s = 7.86325384204

Angle ∠ A = α = 94.94399211322° = 94°56'24″ = 1.65770142153 rad
Angle ∠ B = β = 48.35496321995° = 48°20'59″ = 0.8443860274 rad
Angle ∠ C = γ = 36.71104466683° = 36°42'38″ = 0.64107181642 rad

Height: ha = 3
Height: hb = 4
Height: hc = 5

Median: ma = 3.07655534063
Median: mb = 4.91443979434
Median: mc = 5.56334281828

Inradius: r = 1.27765957447
Circumradius: R = 3.35882350609

Vertex coordinates: A[4.0154913236; 0] B[0; 0] C[4.44770740357; 5]
Centroid: CG[2.82106624239; 1.66766666667]
Coordinates of the circumscribed circle: U[2.0077456618; 2.69221851072]
Coordinates of the inscribed circle: I[2.84438968755; 1.27765957447]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 85.06600788678° = 85°3'36″ = 1.65770142153 rad
∠ B' = β' = 131.65503678° = 131°39'1″ = 0.8443860274 rad
∠ C' = γ' = 143.2989553332° = 143°17'22″ = 0.64107181642 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    