# 19 21 21 triangle

### Acute isosceles triangle.

Sides: a = 19   b = 21   c = 21

Area: T = 177.9199047603
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 53.79330926066° = 53°47'35″ = 0.93988665808 rad
Angle ∠ B = β = 63.10334536967° = 63°6'12″ = 1.10113630364 rad
Angle ∠ C = γ = 63.10334536967° = 63°6'12″ = 1.10113630364 rad

Height: ha = 18.72883208003
Height: hb = 16.94546712003
Height: hc = 16.94546712003

Median: ma = 18.72883208003
Median: mb = 17.0511392905
Median: mc = 17.0511392905

Inradius: r = 5.83334113968
Circumradius: R = 11.77436129336

Vertex coordinates: A[21; 0] B[0; 0] C[8.59552380952; 16.94546712003]
Centroid: CG[9.86550793651; 5.64882237334]
Coordinates of the circumscribed circle: U[10.5; 5.32661582319]
Coordinates of the inscribed circle: I[9.5; 5.83334113968]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.2076907393° = 126°12'25″ = 0.93988665808 rad
∠ B' = β' = 116.8976546303° = 116°53'48″ = 1.10113630364 rad
∠ C' = γ' = 116.8976546303° = 116°53'48″ = 1.10113630364 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    