# 5 8 12 triangle

### Obtuse scalene triangle.

Sides: a = 5   b = 8   c = 12

Area: T = 14.52436875483
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 17.61224390704° = 17°36'45″ = 0.30773950511 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 133.4332536558° = 133°25'57″ = 2.32988370922 rad

Height: ha = 5.80994750193
Height: hb = 3.63109218871
Height: hc = 2.42106145914

Median: ma = 9.88768599666
Median: mb = 8.27664726786
Median: mc = 2.91554759474

Inradius: r = 1.16218950039
Circumradius: R = 8.26223644719

Vertex coordinates: A[12; 0] B[0; 0] C[4.375; 2.42106145914]
Centroid: CG[5.45883333333; 0.80768715305]
Coordinates of the circumscribed circle: U[6; -5.68803755744]
Coordinates of the inscribed circle: I[4.5; 1.16218950039]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.388756093° = 162°23'15″ = 0.30773950511 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 46.56774634422° = 46°34'3″ = 2.32988370922 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    