# 12 13 15 triangle

### Acute scalene triangle.

Sides: a = 12   b = 13   c = 15

Area: T = 74.83331477355
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 50.132165845° = 50°7'54″ = 0.87549624994 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 73.61773301459° = 73°37'2″ = 1.28548647976 rad

Height: ha = 12.47221912892
Height: hb = 11.51327919593
Height: hc = 9.97877530314

Median: ma = 12.68985775404
Median: mb = 11.92768604419
Median: mc = 10.01224921973

Inradius: r = 3.74216573868
Circumradius: R = 7.81773913259

Vertex coordinates: A[15; 0] B[0; 0] C[6.66766666667; 9.97877530314]
Centroid: CG[7.22222222222; 3.32659176771]
Coordinates of the circumscribed circle: U[7.5; 2.20549052458]
Coordinates of the inscribed circle: I[7; 3.74216573868]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.868834155° = 129°52'6″ = 0.87549624994 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 106.3832669854° = 106°22'58″ = 1.28548647976 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    