# 14 21 21 triangle

### Acute isosceles triangle.

Sides: a = 14   b = 21   c = 21

Area: T = 138.5932929113
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 70.52987793655° = 70°31'44″ = 1.23109594173 rad

Height: ha = 19.79989898732
Height: hb = 13.19993265821
Height: hc = 13.19993265821

Median: ma = 19.79989898732
Median: mb = 14.43108696897
Median: mc = 14.43108696897

Inradius: r = 4.95497474683
Circumradius: R = 11.13769318037

Vertex coordinates: A[21; 0] B[0; 0] C[4.66766666667; 13.19993265821]
Centroid: CG[8.55655555556; 4.43997755274]
Coordinates of the circumscribed circle: U[10.5; 3.71223106012]
Coordinates of the inscribed circle: I[7; 4.95497474683]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 109.4711220634° = 109°28'16″ = 1.23109594173 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    