# 9 16 21 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 16   c = 21

Area: T = 67.14216413264
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 23.55664643091° = 23°33'23″ = 0.41111378623 rad
Angle ∠ B = β = 45.27550868451° = 45°16'30″ = 0.79901993346 rad
Angle ∠ C = γ = 111.1688448846° = 111°10'6″ = 1.94402554567 rad

Height: ha = 14.92203647392
Height: hb = 8.39327051658
Height: hc = 6.39444420311

Median: ma = 18.1187670932
Median: mb = 14.03656688476
Median: mc = 7.63221687612

Inradius: r = 2.91992017968
Circumradius: R = 11.26597783591

Vertex coordinates: A[21; 0] B[0; 0] C[6.33333333333; 6.39444420311]
Centroid: CG[9.11111111111; 2.1311480677]
Coordinates of the circumscribed circle: U[10.5; -4.06660310741]
Coordinates of the inscribed circle: I[7; 2.91992017968]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4443535691° = 156°26'37″ = 0.41111378623 rad
∠ B' = β' = 134.7254913155° = 134°43'30″ = 0.79901993346 rad
∠ C' = γ' = 68.83215511542° = 68°49'54″ = 1.94402554567 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    