# 13 24 25 triangle

### Acute scalene triangle.

Sides: a = 13   b = 24   c = 25

Area: T = 153.0888209866
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 30.6833417109° = 30°41' = 0.53655266543 rad
Angle ∠ B = β = 70.4044072102° = 70°24'15″ = 1.2298782865 rad
Angle ∠ C = γ = 78.9132510789° = 78°54'45″ = 1.37772831343 rad

Height: ha = 23.55220322871
Height: hb = 12.75773508222
Height: hc = 12.24770567893

Median: ma = 23.62773147014
Median: mb = 15.90659737206
Median: mc = 14.70554411699

Inradius: r = 4.93883293505
Circumradius: R = 12.73877542771

Vertex coordinates: A[25; 0] B[0; 0] C[4.36; 12.24770567893]
Centroid: CG[9.78766666667; 4.08223522631]
Coordinates of the circumscribed circle: U[12.5; 2.45495681302]
Coordinates of the inscribed circle: I[7; 4.93883293505]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.3176582891° = 149°19' = 0.53655266543 rad
∠ B' = β' = 109.5965927898° = 109°35'45″ = 1.2298782865 rad
∠ C' = γ' = 101.0877489211° = 101°5'15″ = 1.37772831343 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    