# 21 27 28 triangle

### Acute scalene triangle.

Sides: a = 21   b = 27   c = 28

Area: T = 266.5710816107
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 44.84768191535° = 44°50'49″ = 0.78327246533 rad
Angle ∠ B = β = 65.05436961589° = 65°3'13″ = 1.13554011886 rad
Angle ∠ C = γ = 70.09994846876° = 70°5'58″ = 1.22334668118 rad

Height: ha = 25.38876967721
Height: hb = 19.74659863783
Height: hc = 19.04107725791

Median: ma = 25.42114476378
Median: mb = 20.74224685127
Median: mc = 19.72330829233

Inradius: r = 7.01550214765
Circumradius: R = 14.88991017327

Vertex coordinates: A[28; 0] B[0; 0] C[8.85771428571; 19.04107725791]
Centroid: CG[12.28657142857; 6.3476924193]
Coordinates of the circumscribed circle: U[14; 5.06880716656]
Coordinates of the inscribed circle: I[11; 7.01550214765]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.1533180846° = 135°9'11″ = 0.78327246533 rad
∠ B' = β' = 114.9466303841° = 114°56'47″ = 1.13554011886 rad
∠ C' = γ' = 109.9010515312° = 109°54'2″ = 1.22334668118 rad

# How did we calculate this triangle?

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. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    