# 15 15 19 triangle

### Acute isosceles triangle.

Sides: a = 15   b = 15   c = 19

Area: T = 110.2787774279
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 50.70435197608° = 50°42'13″ = 0.88549433622 rad
Angle ∠ B = β = 50.70435197608° = 50°42'13″ = 0.88549433622 rad
Angle ∠ C = γ = 78.59329604784° = 78°35'35″ = 1.37217059292 rad

Height: ha = 14.70437032372
Height: hb = 14.70437032372
Height: hc = 11.60881867662

Median: ma = 15.38766825534
Median: mb = 15.38766825534
Median: mc = 11.60881867662

Inradius: r = 4.50111336441
Circumradius: R = 9.69114360757

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 11.60881867662]
Centroid: CG[9.5; 3.86993955887]
Coordinates of the circumscribed circle: U[9.5; 1.91767506905]
Coordinates of the inscribed circle: I[9.5; 4.50111336441]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.2966480239° = 129°17'47″ = 0.88549433622 rad
∠ B' = β' = 129.2966480239° = 129°17'47″ = 0.88549433622 rad
∠ C' = γ' = 101.4077039522° = 101°24'25″ = 1.37217059292 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    