# 21 21 27 triangle

### Acute isosceles triangle.

Sides: a = 21   b = 21   c = 27

Area: T = 217.1577057219
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 49.99547991151° = 49°59'41″ = 0.87325738534 rad
Angle ∠ B = β = 49.99547991151° = 49°59'41″ = 0.87325738534 rad
Angle ∠ C = γ = 80.01104017697° = 80°37″ = 1.39664449467 rad

Height: ha = 20.6821624497
Height: hb = 20.6821624497
Height: hc = 16.08657079421

Median: ma = 21.78987585695
Median: mb = 21.78987585695
Median: mc = 16.08657079421

Inradius: r = 6.29444074556
Circumradius: R = 13.70878206811

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 16.08657079421]
Centroid: CG[13.5; 5.36219026474]
Coordinates of the circumscribed circle: U[13.5; 2.3787887261]
Coordinates of the inscribed circle: I[13.5; 6.29444074556]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.0055200885° = 130°19″ = 0.87325738534 rad
∠ B' = β' = 130.0055200885° = 130°19″ = 0.87325738534 rad
∠ C' = γ' = 99.99895982303° = 99°59'23″ = 1.39664449467 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    