# 8 19 24 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 19   c = 24

Area: T = 65.96216365776
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 16.81663773207° = 16°48'59″ = 0.29435011525 rad
Angle ∠ B = β = 43.40110149198° = 43°24'4″ = 0.75774906091 rad
Angle ∠ C = γ = 119.7832607759° = 119°46'57″ = 2.0910600892 rad

Height: ha = 16.49904091444
Height: hb = 6.94333301661
Height: hc = 5.49768030481

Median: ma = 21.27220473862
Median: mb = 15.15875063912
Median: mc = 8.27664726786

Inradius: r = 2.58767308462
Circumradius: R = 13.82662185009

Vertex coordinates: A[24; 0] B[0; 0] C[5.81325; 5.49768030481]
Centroid: CG[9.93875; 1.83222676827]
Coordinates of the circumscribed circle: U[12; -6.86876282685]
Coordinates of the inscribed circle: I[6.5; 2.58767308462]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.1843622679° = 163°11'1″ = 0.29435011525 rad
∠ B' = β' = 136.599898508° = 136°35'56″ = 0.75774906091 rad
∠ C' = γ' = 60.21773922406° = 60°13'3″ = 2.0910600892 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    