# 9 17 21 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 17   c = 21

Area: T = 74.41222805725
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 24.63774826477° = 24°38'15″ = 0.43300051916 rad
Angle ∠ B = β = 51.94661286461° = 51°56'46″ = 0.90766309785 rad
Angle ∠ C = γ = 103.4166388706° = 103°24'59″ = 1.80549564834 rad

Height: ha = 16.53660623494
Height: hb = 8.75443859497
Height: hc = 7.0876883864

Median: ma = 18.56774446276
Median: mb = 13.7398631664
Median: mc = 8.64658082329

Inradius: r = 3.16664800244
Circumradius: R = 10.79545891971

Vertex coordinates: A[21; 0] B[0; 0] C[5.54876190476; 7.0876883864]
Centroid: CG[8.84992063492; 2.36222946213]
Coordinates of the circumscribed circle: U[10.5; -2.50546269052]
Coordinates of the inscribed circle: I[6.5; 3.16664800244]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3632517352° = 155°21'45″ = 0.43300051916 rad
∠ B' = β' = 128.0543871354° = 128°3'14″ = 0.90766309785 rad
∠ C' = γ' = 76.58436112938° = 76°35'1″ = 1.80549564834 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    