# 174 138 188 triangle

### Acute scalene triangle.

Sides: a = 174   b = 138   c = 188

Area: T = 11486.34397129
Perimeter: p = 500
Semiperimeter: s = 250

Angle ∠ A = α = 62.31096326608° = 62°18'35″ = 1.08875082456 rad
Angle ∠ B = β = 44.60994683749° = 44°36'34″ = 0.77985821007 rad
Angle ∠ C = γ = 73.08108989643° = 73°4'51″ = 1.27655023072 rad

Height: ha = 132.0276893252
Height: hb = 166.4698691491
Height: hc = 122.1955103329

Median: ma = 140.0899257261
Median: mb = 167.4788356811
Median: mc = 125.7933481548

Inradius: r = 45.94553588516
Circumradius: R = 98.25327095845

Vertex coordinates: A[188; 0] B[0; 0] C[123.8722340425; 122.1955103329]
Centroid: CG[103.9577446808; 40.73217011096]
Coordinates of the circumscribed circle: U[94; 28.59436171321]
Coordinates of the inscribed circle: I[112; 45.94553588516]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.6990367339° = 117°41'25″ = 1.08875082456 rad
∠ B' = β' = 135.3910531625° = 135°23'26″ = 0.77985821007 rad
∠ C' = γ' = 106.9199101036° = 106°55'9″ = 1.27655023072 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    