# 4 21 23 triangle

### Obtuse scalene triangle.

Sides: a = 4   b = 21   c = 23

Area: T = 37.9477331922
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 9.04404551853° = 9°2'26″ = 0.15877857089 rad
Angle ∠ B = β = 55.58326112896° = 55°34'57″ = 0.97700995739 rad
Angle ∠ C = γ = 115.3776933525° = 115°22'37″ = 2.01437073709 rad

Height: ha = 18.9743665961
Height: hb = 3.61440316116
Height: hc = 3.32997679932

Median: ma = 21.93217121995
Median: mb = 12.73877392029
Median: mc = 9.81107084352

Inradius: r = 1.58111388301
Circumradius: R = 12.72881675822

Vertex coordinates: A[23; 0] B[0; 0] C[2.26108695652; 3.32997679932]
Centroid: CG[8.42202898551; 1.10999226644]
Coordinates of the circumscribed circle: U[11.5; -5.45549289638]
Coordinates of the inscribed circle: I[3; 1.58111388301]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.9659544815° = 170°57'34″ = 0.15877857089 rad
∠ B' = β' = 124.417738871° = 124°25'3″ = 0.97700995739 rad
∠ C' = γ' = 64.62330664748° = 64°37'23″ = 2.01437073709 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    