# 9 21 27 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 21   c = 27

Area: T = 79.07107752586
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 16.1955116739° = 16°11'42″ = 0.28326581098 rad
Angle ∠ B = β = 40.60110607311° = 40°36'4″ = 0.70986221896 rad
Angle ∠ C = γ = 123.204382253° = 123°12'14″ = 2.15503123542 rad

Height: ha = 17.57112833908
Height: hb = 7.53105500246
Height: hc = 5.85770944636

Median: ma = 23.76444692766
Median: mb = 17.16882847134
Median: mc = 8.87441196746

Inradius: r = 2.7744413167
Circumradius: R = 16.13442796479

Vertex coordinates: A[27; 0] B[0; 0] C[6.83333333333; 5.85770944636]
Centroid: CG[11.27877777778; 1.95223648212]
Coordinates of the circumscribed circle: U[13.5; -8.83554388548]
Coordinates of the inscribed circle: I[7.5; 2.7744413167]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8054883261° = 163°48'18″ = 0.28326581098 rad
∠ B' = β' = 139.3998939269° = 139°23'56″ = 0.70986221896 rad
∠ C' = γ' = 56.796617747° = 56°47'46″ = 2.15503123542 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    