# 12 18 21 triangle

### Acute scalene triangle.

Sides: a = 12   b = 18   c = 21

Area: T = 107.7898856103
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 34.77219440319° = 34°46'19″ = 0.60768849107 rad
Angle ∠ B = β = 58.81113776665° = 58°48'41″ = 1.02664521779 rad
Angle ∠ C = γ = 86.41766783015° = 86°25' = 1.5088255565 rad

Height: ha = 17.96548093505
Height: hb = 11.9776539567
Height: hc = 10.26656053431

Median: ma = 18.6154510469
Median: mb = 14.54330395722
Median: mc = 11.12442977306

Inradius: r = 4.22770139648
Circumradius: R = 10.52105680902

Vertex coordinates: A[21; 0] B[0; 0] C[6.21442857143; 10.26656053431]
Centroid: CG[9.07114285714; 3.42218684477]
Coordinates of the circumscribed circle: U[10.5; 0.65875355056]
Coordinates of the inscribed circle: I[7.5; 4.22770139648]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2288055968° = 145°13'41″ = 0.60768849107 rad
∠ B' = β' = 121.1898622333° = 121°11'19″ = 1.02664521779 rad
∠ C' = γ' = 93.58333216985° = 93°35' = 1.5088255565 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    