# 420 293 512 triangle

### Acute scalene triangle.

Sides: a = 420   b = 293   c = 512

Area: T = 61529.99444006
Perimeter: p = 1225
Semiperimeter: s = 612.5

Angle ∠ A = α = 55.11660809659° = 55°6'58″ = 0.96219570837 rad
Angle ∠ B = β = 34.90883626268° = 34°54'30″ = 0.60992658643 rad
Angle ∠ C = γ = 89.97655564073° = 89°58'32″ = 1.57703697056 rad

Height: ha = 2932.999973336
Height: hb = 4209.999961779
Height: hc = 240.3521540627

Median: ma = 360.4121570292
Median: mb = 444.7588080309
Median: mc = 256.1032518535

Inradius: r = 100.4577133715
Circumradius: R = 2566.000023297

Vertex coordinates: A[512; 0] B[0; 0] C[344.4298710938; 240.3521540627]
Centroid: CG[285.4766236979; 80.11771802091]
Coordinates of the circumscribed circle: U[256; 0.1099215027]
Coordinates of the inscribed circle: I[319.5; 100.4577133715]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.8843919034° = 124°53'2″ = 0.96219570837 rad
∠ B' = β' = 145.0921637373° = 145°5'30″ = 0.60992658643 rad
∠ C' = γ' = 90.02444435927° = 90°1'28″ = 1.57703697056 rad

# How did we calculate this triangle?

### 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    