# 15 27 28 triangle

### Acute scalene triangle.

Sides: a = 15   b = 27   c = 28

Area: T = 197.9989898732
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 31.58663380965° = 31°35'11″ = 0.55112855984 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 77.8854882538° = 77°53'6″ = 1.35993476378 rad

Height: ha = 26.39986531643
Height: hb = 14.66659184246
Height: hc = 14.14221356237

Median: ma = 26.46222372448
Median: mb = 17.9511323071
Median: mc = 16.76330546142

Inradius: r = 5.65768542495
Circumradius: R = 14.3198912319

Vertex coordinates: A[28; 0] B[0; 0] C[5; 14.14221356237]
Centroid: CG[11; 4.71440452079]
Coordinates of the circumscribed circle: U[14; 3.005520382]
Coordinates of the inscribed circle: I[8; 5.65768542495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.4143661903° = 148°24'49″ = 0.55112855984 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 102.1155117462° = 102°6'54″ = 1.35993476378 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    