# 20 20 30 triangle

### Obtuse isosceles triangle.

Sides: a = 20   b = 20   c = 30

Area: T = 198.431134833
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 19.8433134833
Height: hb = 19.8433134833
Height: hc = 13.22987565553

Median: ma = 23.45220787991
Median: mb = 23.45220787991
Median: mc = 13.22987565553

Inradius: r = 5.66994670951
Circumradius: R = 15.11985789204

Vertex coordinates: A[30; 0] B[0; 0] C[15; 13.22987565553]
Centroid: CG[15; 4.41095855184]
Coordinates of the circumscribed circle: U[15; -1.8989822365]
Coordinates of the inscribed circle: I[15; 5.66994670951]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 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    