# 14 24 24 triangle

### Acute isosceles triangle.

Sides: a = 14   b = 24   c = 24

Area: T = 160.6955363966
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 33.91655266° = 33°54'56″ = 0.59219376067 rad
Angle ∠ B = β = 73.04222367° = 73°2'32″ = 1.27548275234 rad
Angle ∠ C = γ = 73.04222367° = 73°2'32″ = 1.27548275234 rad

Height: ha = 22.95664805665
Height: hb = 13.39112803305
Height: hc = 13.39112803305

Median: ma = 22.95664805665
Median: mb = 15.55663491861
Median: mc = 15.55663491861

Inradius: r = 5.18437214182
Circumradius: R = 12.54554770458

Vertex coordinates: A[24; 0] B[0; 0] C[4.08333333333; 13.39112803305]
Centroid: CG[9.36111111111; 4.46437601102]
Coordinates of the circumscribed circle: U[12; 3.65990974717]
Coordinates of the inscribed circle: I[7; 5.18437214182]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.08444734° = 146°5'4″ = 0.59219376067 rad
∠ B' = β' = 106.95877633° = 106°57'28″ = 1.27548275234 rad
∠ C' = γ' = 106.95877633° = 106°57'28″ = 1.27548275234 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    