# 8 21 21 triangle

### Acute isosceles triangle.

Sides: a = 8   b = 21   c = 21

Area: T = 82.46221125124
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 21.96111508552° = 21°57'40″ = 0.383329439 rad
Angle ∠ B = β = 79.01994245724° = 79°1'10″ = 1.37991491318 rad
Angle ∠ C = γ = 79.01994245724° = 79°1'10″ = 1.37991491318 rad

Height: ha = 20.61655281281
Height: hb = 7.8543534525
Height: hc = 7.8543534525

Median: ma = 20.61655281281
Median: mb = 11.92768604419
Median: mc = 11.92768604419

Inradius: r = 3.29884845005
Circumradius: R = 10.69658210641

Vertex coordinates: A[21; 0] B[0; 0] C[1.52438095238; 7.8543534525]
Centroid: CG[7.50879365079; 2.61878448417]
Coordinates of the circumscribed circle: U[10.5; 2.03772992503]
Coordinates of the inscribed circle: I[4; 3.29884845005]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.0398849145° = 158°2'20″ = 0.383329439 rad
∠ B' = β' = 100.9810575428° = 100°58'50″ = 1.37991491318 rad
∠ C' = γ' = 100.9810575428° = 100°58'50″ = 1.37991491318 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    