# 65 72 96 triangle

### Acute scalene triangle.

Sides: a = 65   b = 72   c = 96

Area: T = 2339.502249786
Perimeter: p = 233
Semiperimeter: s = 116.5

Angle ∠ A = α = 42.60549358939° = 42°36'18″ = 0.74435964089 rad
Angle ∠ B = β = 48.57765672248° = 48°34'36″ = 0.84878210374 rad
Angle ∠ C = γ = 88.81884968813° = 88°49'7″ = 1.55501752073 rad

Height: ha = 71.98546922419
Height: hb = 64.98661804962
Height: hc = 48.74396353721

Median: ma = 78.3822077033
Median: mb = 73.65112050139
Median: mc = 48.99548976935

Inradius: r = 20.08215665052
Circumradius: R = 48.01102073422

Vertex coordinates: A[96; 0] B[0; 0] C[43.00552083333; 48.74396353721]
Centroid: CG[46.33550694444; 16.2476545124]
Coordinates of the circumscribed circle: U[48; 0.99899540617]
Coordinates of the inscribed circle: I[44.5; 20.08215665052]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.3955064106° = 137°23'42″ = 0.74435964089 rad
∠ B' = β' = 131.4233432775° = 131°25'24″ = 0.84878210374 rad
∠ C' = γ' = 91.18215031187° = 91°10'53″ = 1.55501752073 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    