# 7 21 23 triangle

### Obtuse scalene triangle.

Sides: a = 7   b = 21   c = 23

Area: T = 72.85504461208
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 17.55772234277° = 17°33'26″ = 0.30664313563 rad
Angle ∠ B = β = 64.82198469684° = 64°49'11″ = 1.13113197502 rad
Angle ∠ C = γ = 97.62329296039° = 97°37'23″ = 1.7043841547 rad

Height: ha = 20.81444131774
Height: hb = 6.93881377258
Height: hc = 6.33548214018

Median: ma = 21.74328149052
Median: mb = 13.37697419571
Median: mc = 10.61883802908

Inradius: r = 2.857688024
Circumradius: R = 11.60325370469

Vertex coordinates: A[23; 0] B[0; 0] C[2.97882608696; 6.33548214018]
Centroid: CG[8.65994202899; 2.11216071339]
Coordinates of the circumscribed circle: U[11.5; -1.53991120572]
Coordinates of the inscribed circle: I[4.5; 2.857688024]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.4432776572° = 162°26'34″ = 0.30664313563 rad
∠ B' = β' = 115.1880153032° = 115°10'49″ = 1.13113197502 rad
∠ C' = γ' = 82.37770703961° = 82°22'37″ = 1.7043841547 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    