# 17 19 19 triangle

### Acute isosceles triangle.

Sides: a = 17   b = 19   c = 19

Area: T = 144.4377486478
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 53.1549939038° = 53°9' = 0.92876414334 rad
Angle ∠ B = β = 63.4255030481° = 63°25'30″ = 1.10769756101 rad
Angle ∠ C = γ = 63.4255030481° = 63°25'30″ = 1.10769756101 rad

Height: ha = 16.9932645468
Height: hb = 15.2043945945
Height: hc = 15.2043945945

Median: ma = 16.9932645468
Median: mb = 15.3221553446
Median: mc = 15.3221553446

Inradius: r = 5.25222722356
Circumradius: R = 10.62222424484

Vertex coordinates: A[19; 0] B[0; 0] C[7.60552631579; 15.2043945945]
Centroid: CG[8.86884210526; 5.06879819817]
Coordinates of the circumscribed circle: U[9.5; 4.75220558322]
Coordinates of the inscribed circle: I[8.5; 5.25222722356]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.8550060962° = 126°51' = 0.92876414334 rad
∠ B' = β' = 116.5754969519° = 116°34'30″ = 1.10769756101 rad
∠ C' = γ' = 116.5754969519° = 116°34'30″ = 1.10769756101 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    