# 23 25 29 triangle

### Acute scalene triangle.

Sides: a = 23   b = 25   c = 29

Area: T = 276.6466322043
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 49.74437751503° = 49°44'38″ = 0.86881926587 rad
Angle ∠ B = β = 56.05498932346° = 56°3' = 0.97882551823 rad
Angle ∠ C = γ = 74.20663316151° = 74°12'23″ = 1.29551448125 rad

Height: ha = 24.05662019168
Height: hb = 22.13217057635
Height: hc = 19.07990566926

Median: ma = 24.51102019576
Median: mb = 22.99545645751
Median: mc = 19.15107180022

Inradius: r = 7.18656187544
Circumradius: R = 15.06988791711

Vertex coordinates: A[29; 0] B[0; 0] C[12.84548275862; 19.07990566926]
Centroid: CG[13.94882758621; 6.36596855642]
Coordinates of the circumscribed circle: U[14.5; 4.10113558092]
Coordinates of the inscribed circle: I[13.5; 7.18656187544]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.256622485° = 130°15'22″ = 0.86881926587 rad
∠ B' = β' = 123.9550106765° = 123°57' = 0.97882551823 rad
∠ C' = γ' = 105.7943668385° = 105°47'37″ = 1.29551448125 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    