# 9 17 19 triangle

### Acute scalene triangle.

Sides: a = 9   b = 17   c = 19

Area: T = 76.46769046058
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 28.26603825592° = 28°15'37″ = 0.49332367235 rad
Angle ∠ B = β = 63.4255030481° = 63°25'30″ = 1.10769756101 rad
Angle ∠ C = γ = 88.31545869598° = 88°18'53″ = 1.541138032 rad

Height: ha = 16.9932645468
Height: hb = 8.99661064242
Height: hc = 8.04991478532

Median: ma = 17.45770902501
Median: mb = 12.19663109177
Median: mc = 9.7343961167

Inradius: r = 3.39985290936
Circumradius: R = 9.50441116643

Vertex coordinates: A[19; 0] B[0; 0] C[4.02663157895; 8.04991478532]
Centroid: CG[7.67554385965; 2.68330492844]
Coordinates of the circumscribed circle: U[9.5; 0.2879532696]
Coordinates of the inscribed circle: I[5.5; 3.39985290936]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.7439617441° = 151°44'23″ = 0.49332367235 rad
∠ B' = β' = 116.5754969519° = 116°34'30″ = 1.10769756101 rad
∠ C' = γ' = 91.68554130402° = 91°41'7″ = 1.541138032 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    