# 20 24 24 triangle

### Acute isosceles triangle.

Sides: a = 20   b = 24   c = 24

Area: T = 218.1744242293
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 49.24986367043° = 49°14'55″ = 0.86595508626 rad
Angle ∠ B = β = 65.37656816478° = 65°22'32″ = 1.14110208955 rad
Angle ∠ C = γ = 65.37656816478° = 65°22'32″ = 1.14110208955 rad

Height: ha = 21.81774242293
Height: hb = 18.18111868577
Height: hc = 18.18111868577

Median: ma = 21.81774242293
Median: mb = 18.5477236991
Median: mc = 18.5477236991

Inradius: r = 6.41768894792
Circumradius: R = 13.22004583572

Vertex coordinates: A[24; 0] B[0; 0] C[8.33333333333; 18.18111868577]
Centroid: CG[10.77877777778; 6.06603956192]
Coordinates of the circumscribed circle: U[12; 5.55001909822]
Coordinates of the inscribed circle: I[10; 6.41768894792]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.7511363296° = 130°45'5″ = 0.86595508626 rad
∠ B' = β' = 114.6244318352° = 114°37'28″ = 1.14110208955 rad
∠ C' = γ' = 114.6244318352° = 114°37'28″ = 1.14110208955 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    