# 5 20 20 triangle

### Acute isosceles triangle.

Sides: a = 5   b = 20   c = 20

Area: T = 49.60878370825
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 14.36215115629° = 14°21'41″ = 0.25106556623 rad
Angle ∠ B = β = 82.81992442185° = 82°49'9″ = 1.44554684956 rad
Angle ∠ C = γ = 82.81992442185° = 82°49'9″ = 1.44554684956 rad

Height: ha = 19.8433134833
Height: hb = 4.96107837082
Height: hc = 4.96107837082

Median: ma = 19.8433134833
Median: mb = 10.60766017178
Median: mc = 10.60766017178

Inradius: r = 2.20547927592
Circumradius: R = 10.07990526136

Vertex coordinates: A[20; 0] B[0; 0] C[0.625; 4.96107837082]
Centroid: CG[6.875; 1.65435945694]
Coordinates of the circumscribed circle: U[10; 1.26598815767]
Coordinates of the inscribed circle: I[2.5; 2.20547927592]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6388488437° = 165°38'19″ = 0.25106556623 rad
∠ B' = β' = 97.18107557815° = 97°10'51″ = 1.44554684956 rad
∠ C' = γ' = 97.18107557815° = 97°10'51″ = 1.44554684956 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    