# 9 20 27 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 20   c = 27

Area: T = 65.23880257212
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 13.98223106495° = 13°58'56″ = 0.24440373579 rad
Angle ∠ B = β = 32.47554703224° = 32°28'32″ = 0.56768038833 rad
Angle ∠ C = γ = 133.5422219028° = 133°32'32″ = 2.33107514125 rad

Height: ha = 14.49773390492
Height: hb = 6.52438025721
Height: hc = 4.83224463497

Median: ma = 23.32991662946
Median: mb = 17.46442491966
Median: mc = 7.63221687612

Inradius: r = 2.332992949
Circumradius: R = 18.62441074369

Vertex coordinates: A[27; 0] B[0; 0] C[7.59325925926; 4.83224463497]
Centroid: CG[11.53108641975; 1.61108154499]
Coordinates of the circumscribed circle: U[13.5; -12.83299406787]
Coordinates of the inscribed circle: I[8; 2.332992949]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.0187689351° = 166°1'4″ = 0.24440373579 rad
∠ B' = β' = 147.5254529678° = 147°31'28″ = 0.56768038833 rad
∠ C' = γ' = 46.45877809718° = 46°27'28″ = 2.33107514125 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    