# 13 15 24 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 15   c = 24

Area: T = 86.23222445492
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 28.62545509534° = 28°37'28″ = 0.5499592661 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 117.8188139285° = 117°49'5″ = 2.05663144491 rad

Height: ha = 13.26664991614
Height: hb = 11.49876326066
Height: hc = 7.18660203791

Median: ma = 18.92774932307
Median: mb = 17.78334192438
Median: mc = 7.28801098893

Inradius: r = 3.31766247904
Circumradius: R = 13.5688010506

Vertex coordinates: A[24; 0] B[0; 0] C[10.83333333333; 7.18660203791]
Centroid: CG[11.61111111111; 2.39553401264]
Coordinates of the circumscribed circle: U[12; -6.33217382361]
Coordinates of the inscribed circle: I[11; 3.31766247904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.3755449047° = 151°22'32″ = 0.5499592661 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 62.18218607153° = 62°10'55″ = 2.05663144491 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    