# 12 27 28 triangle

### Acute scalene triangle.

Sides: a = 12   b = 27   c = 28

Area: T = 160.4654754697
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 25.12196477175° = 25°7'11″ = 0.43884205596 rad
Angle ∠ B = β = 72.7754633383° = 72°46'29″ = 1.27701569645 rad
Angle ∠ C = γ = 82.10657188995° = 82°6'21″ = 1.43330151295 rad

Height: ha = 26.74441257828
Height: hb = 11.88662781257
Height: hc = 11.46217681926

Median: ma = 26.84221310629
Median: mb = 16.78554103316
Median: mc = 15.50880624193

Inradius: r = 4.79899926775
Circumradius: R = 14.1343944892

Vertex coordinates: A[28; 0] B[0; 0] C[3.55435714286; 11.46217681926]
Centroid: CG[10.51878571429; 3.82105893975]
Coordinates of the circumscribed circle: U[14; 1.94112362583]
Coordinates of the inscribed circle: I[6.5; 4.79899926775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.8880352282° = 154°52'49″ = 0.43884205596 rad
∠ B' = β' = 107.2255366617° = 107°13'31″ = 1.27701569645 rad
∠ C' = γ' = 97.89442811005° = 97°53'39″ = 1.43330151295 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    