# Triangle calculator

You have entered height hc, angle α, angle β and angle γ.

### Acute isosceles triangle.

Sides: a = 55.16988959481   b = 55.16988959481   c = 46.63107658155

Area: T = 1165.769914539
Perimeter: p = 156.9698557712
Semiperimeter: s = 78.48442788559

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

Height: ha = 42.26218261741
Height: hb = 42.26218261741
Height: hc = 50

Median: ma = 42.99897188907
Median: mb = 42.99897188907
Median: mc = 50

Vertex coordinates: A[46.63107658155; 0] B[0; 0] C[23.31553829077; 50]
Centroid: CG[23.31553829077; 16.66766666667]
Coordinates of the circumscribed circle: U[23.31553829077; 19.56439291987]
Coordinates of the inscribed circle: I[23.31553829077; 14.85435370699]

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    