# 12 15 21 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 15   c = 21

Area: T = 88.18216307402
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 34.048773237° = 34°2'52″ = 0.59442450327 rad
Angle ∠ B = β = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ C = γ = 101.5376959033° = 101°32'13″ = 1.77221542476 rad

Height: ha = 14.69769384567
Height: hb = 11.75875507654
Height: hc = 8.39882505467

Median: ma = 17.23436879396
Median: mb = 15.37704261489
Median: mc = 8.61768439698

Inradius: r = 3.67442346142
Circumradius: R = 10.71765176247

Vertex coordinates: A[21; 0] B[0; 0] C[8.57114285714; 8.39882505467]
Centroid: CG[9.85771428571; 2.79994168489]
Coordinates of the circumscribed circle: U[10.5; -2.14333035249]
Coordinates of the inscribed circle: I[9; 3.67442346142]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.952226763° = 145°57'8″ = 0.59442450327 rad
∠ B' = β' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ C' = γ' = 78.46330409672° = 78°27'47″ = 1.77221542476 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    