# 7 21 27 triangle

### Obtuse scalene triangle.

Sides: a = 7   b = 21   c = 27

Area: T = 42.80440593869
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 8.68439745947° = 8°41'2″ = 0.15215639488 rad
Angle ∠ B = β = 26.93333044068° = 26°56' = 0.47700748403 rad
Angle ∠ C = γ = 144.3832720999° = 144°22'58″ = 2.52199538644 rad

Height: ha = 12.23297312534
Height: hb = 4.07765770845
Height: hc = 3.17106710657

Median: ma = 23.93221958875
Median: mb = 16.69658078571
Median: mc = 7.92114897589

Inradius: r = 1.55765112504
Circumradius: R = 23.18112125815

Vertex coordinates: A[27; 0] B[0; 0] C[6.24107407407; 3.17106710657]
Centroid: CG[11.08802469136; 1.05768903552]
Coordinates of the circumscribed circle: U[13.5; -18.84545911802]
Coordinates of the inscribed circle: I[6.5; 1.55765112504]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.3166025405° = 171°18'58″ = 0.15215639488 rad
∠ B' = β' = 153.0676695593° = 153°4' = 0.47700748403 rad
∠ C' = γ' = 35.61772790015° = 35°37'2″ = 2.52199538644 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    