# 8 12 16 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 12   c = 16

Area: T = 46.47658001545
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 11.61989500386
Height: hb = 7.74659666924
Height: hc = 5.80994750193

Median: ma = 13.56546599663
Median: mb = 11.13655287257
Median: mc = 6.32545553203

Inradius: r = 2.58219888975
Circumradius: R = 8.26223644719

Vertex coordinates: A[16; 0] B[0; 0] C[5.5; 5.80994750193]
Centroid: CG[7.16766666667; 1.93664916731]
Coordinates of the circumscribed circle: U[8; -2.0665591118]
Coordinates of the inscribed circle: I[6; 2.58219888975]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 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    