# 8 10 13 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 10   c = 13

Area: T = 39.98804639793
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 37.95880285807° = 37°57'29″ = 0.66224925763 rad
Angle ∠ B = β = 50.251118676° = 50°15'4″ = 0.8777048662 rad
Angle ∠ C = γ = 91.79107846593° = 91°47'27″ = 1.60220514153 rad

Height: ha = 9.99551159948
Height: hb = 7.99660927959
Height: hc = 6.15108406122

Median: ma = 10.88657705285
Median: mb = 9.56655632349
Median: mc = 6.30547601065

Inradius: r = 2.57993847729
Circumradius: R = 6.50331761546

Vertex coordinates: A[13; 0] B[0; 0] C[5.11553846154; 6.15108406122]
Centroid: CG[6.03884615385; 2.05502802041]
Coordinates of the circumscribed circle: U[6.5; -0.20332242548]
Coordinates of the inscribed circle: I[5.5; 2.57993847729]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.0421971419° = 142°2'31″ = 0.66224925763 rad
∠ B' = β' = 129.749881324° = 129°44'56″ = 0.8777048662 rad
∠ C' = γ' = 88.20992153407° = 88°12'33″ = 1.60220514153 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    