# 16 26 27 triangle

### Acute scalene triangle.

Sides: a = 16   b = 26   c = 27

Area: T = 201.714375139
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 35.07774391825° = 35°4'39″ = 0.61222168069 rad
Angle ∠ B = β = 69.04547372744° = 69°2'41″ = 1.20550579966 rad
Angle ∠ C = γ = 75.87878235431° = 75°52'40″ = 1.32443178501 rad

Height: ha = 25.21442189238
Height: hb = 15.51664424146
Height: hc = 14.94217593623

Median: ma = 25.2698557537
Median: mb = 17.98661057486
Median: mc = 16.84548805279

Inradius: r = 5.84767754026
Circumradius: R = 13.92107167615

Vertex coordinates: A[27; 0] B[0; 0] C[5.72222222222; 14.94217593623]
Centroid: CG[10.90774074074; 4.98105864541]
Coordinates of the circumscribed circle: U[13.5; 3.39765210368]
Coordinates of the inscribed circle: I[8.5; 5.84767754026]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.9232560818° = 144°55'21″ = 0.61222168069 rad
∠ B' = β' = 110.9555262726° = 110°57'19″ = 1.20550579966 rad
∠ C' = γ' = 104.1222176457° = 104°7'20″ = 1.32443178501 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    