# 16 18 21 triangle

### Acute scalene triangle.

Sides: a = 16   b = 18   c = 21

Area: T = 139.7444185926
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 47.67992428549° = 47°40'45″ = 0.83221597727 rad
Angle ∠ B = β = 56.2855185269° = 56°17'7″ = 0.9822361803 rad
Angle ∠ C = γ = 76.03655718761° = 76°2'8″ = 1.32770710779 rad

Height: ha = 17.46880232407
Height: hb = 15.52771317695
Height: hc = 13.30989700881

Median: ma = 17.84765682976
Median: mb = 16.35554272338
Median: mc = 13.40770876778

Inradius: r = 5.08216067609
Circumradius: R = 10.82197703538

Vertex coordinates: A[21; 0] B[0; 0] C[8.8810952381; 13.30989700881]
Centroid: CG[9.96603174603; 4.43663233627]
Coordinates of the circumscribed circle: U[10.5; 2.61110209708]
Coordinates of the inscribed circle: I[9.5; 5.08216067609]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.3210757145° = 132°19'15″ = 0.83221597727 rad
∠ B' = β' = 123.7154814731° = 123°42'53″ = 0.9822361803 rad
∠ C' = γ' = 103.9644428124° = 103°57'52″ = 1.32770710779 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    