# 10 12 13 triangle

### Acute scalene triangle.

Sides: a = 10   b = 12   c = 13

Area: T = 56.99550655759
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 46.94656106092° = 46°56'44″ = 0.81993554745 rad
Angle ∠ B = β = 61.26443462551° = 61°15'52″ = 1.06992645562 rad
Angle ∠ C = γ = 71.79900431357° = 71°47'24″ = 1.25329726229 rad

Height: ha = 11.39990131152
Height: hb = 9.4999177596
Height: hc = 8.76884716271

Median: ma = 11.46773449412
Median: mb = 9.92547166206
Median: mc = 8.93302855497

Inradius: r = 3.25768608901
Circumradius: R = 6.84326976276

Vertex coordinates: A[13; 0] B[0; 0] C[4.80876923077; 8.76884716271]
Centroid: CG[5.93658974359; 2.92328238757]
Coordinates of the circumscribed circle: U[6.5; 2.13883430086]
Coordinates of the inscribed circle: I[5.5; 3.25768608901]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.0544389391° = 133°3'16″ = 0.81993554745 rad
∠ B' = β' = 118.7365653745° = 118°44'8″ = 1.06992645562 rad
∠ C' = γ' = 108.2109956864° = 108°12'36″ = 1.25329726229 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    