# 9 19 24 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 19   c = 24

Area: T = 78.66438417572
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 20.18328243451° = 20°10'58″ = 0.35222567372 rad
Angle ∠ B = β = 46.75498273458° = 46°44'59″ = 0.81659384119 rad
Angle ∠ C = γ = 113.0677348309° = 113°4'2″ = 1.97333975045 rad

Height: ha = 17.48108537238
Height: hb = 8.28804043955
Height: hc = 6.55553201464

Median: ma = 21.17219153597
Median: mb = 15.43553490404
Median: mc = 8.77549643874

Inradius: r = 3.02655323753
Circumradius: R = 13.0432841248

Vertex coordinates: A[24; 0] B[0; 0] C[6.16766666667; 6.55553201464]
Centroid: CG[10.05655555556; 2.18551067155]
Coordinates of the circumscribed circle: U[12; -5.11103530036]
Coordinates of the inscribed circle: I[7; 3.02655323753]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.8177175655° = 159°49'2″ = 0.35222567372 rad
∠ B' = β' = 133.2550172654° = 133°15'1″ = 0.81659384119 rad
∠ C' = γ' = 66.93326516909° = 66°55'58″ = 1.97333975045 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    