# 9 21 23 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 21   c = 23

Area: T = 94.48437949069
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 23.03215063879° = 23°1'53″ = 0.40219756182 rad
Angle ∠ B = β = 65.90774000045° = 65°54'27″ = 1.15503011315 rad
Angle ∠ C = γ = 91.06110936076° = 91°3'40″ = 1.58993159039 rad

Height: ha = 20.99663988682
Height: hb = 8.99884566578
Height: hc = 8.21659821658

Median: ma = 21.55880611373
Median: mb = 13.9555285737
Median: mc = 11.34768057179

Inradius: r = 3.56554262229
Circumradius: R = 11.50219723866

Vertex coordinates: A[23; 0] B[0; 0] C[3.67439130435; 8.21659821658]
Centroid: CG[8.89113043478; 2.73986607219]
Coordinates of the circumscribed circle: U[11.5; -0.21329994886]
Coordinates of the inscribed circle: I[5.5; 3.56554262229]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9688493612° = 156°58'7″ = 0.40219756182 rad
∠ B' = β' = 114.0932599996° = 114°5'33″ = 1.15503011315 rad
∠ C' = γ' = 88.93989063924° = 88°56'20″ = 1.58993159039 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    