# 4 23 24 triangle

### Obtuse scalene triangle.

Sides: a = 4   b = 23   c = 24

Area: T = 45.34224470006
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 9.4565656367° = 9°27'20″ = 0.16550323365 rad
Angle ∠ B = β = 70.84549899264° = 70°50'42″ = 1.23664783328 rad
Angle ∠ C = γ = 99.69993537065° = 99°41'58″ = 1.74400819843 rad

Height: ha = 22.67112235003
Height: hb = 3.94328214783
Height: hc = 3.779853725

Median: ma = 23.42200768573
Median: mb = 12.79664838921
Median: mc = 11.33657840488

Inradius: r = 1.77881351765
Circumradius: R = 12.17440231619

Vertex coordinates: A[24; 0] B[0; 0] C[1.31325; 3.779853725]
Centroid: CG[8.43875; 1.26595124167]
Coordinates of the circumscribed circle: U[12; -2.05110582501]
Coordinates of the inscribed circle: I[2.5; 1.77881351765]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.5444343633° = 170°32'40″ = 0.16550323365 rad
∠ B' = β' = 109.1555010074° = 109°9'18″ = 1.23664783328 rad
∠ C' = γ' = 80.30106462935° = 80°18'2″ = 1.74400819843 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    