# 5 24 24 triangle

### Acute isosceles triangle.

Sides: a = 5   b = 24   c = 24

Area: T = 59.67435913114
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 11.95883135926° = 11°57'30″ = 0.20987119452 rad
Angle ∠ B = β = 84.02108432037° = 84°1'15″ = 1.46664403542 rad
Angle ∠ C = γ = 84.02108432037° = 84°1'15″ = 1.46664403542 rad

Height: ha = 23.86994365246
Height: hb = 4.9732799276
Height: hc = 4.9732799276

Median: ma = 23.86994365246
Median: mb = 12.51099960032
Median: mc = 12.51099960032

Inradius: r = 2.25218336344
Circumradius: R = 12.06656388224

Vertex coordinates: A[24; 0] B[0; 0] C[0.52108333333; 4.9732799276]
Centroid: CG[8.17436111111; 1.65875997587]
Coordinates of the circumscribed circle: U[12; 1.25768373773]
Coordinates of the inscribed circle: I[2.5; 2.25218336344]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.0421686407° = 168°2'30″ = 0.20987119452 rad
∠ B' = β' = 95.97991567963° = 95°58'45″ = 1.46664403542 rad
∠ C' = γ' = 95.97991567963° = 95°58'45″ = 1.46664403542 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    