# 51 68 85 triangle

### Right scalene Pythagorean triangle.

Sides: a = 51   b = 68   c = 85

Area: T = 1734
Perimeter: p = 204
Semiperimeter: s = 102

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 68
Height: hb = 51
Height: hc = 40.8

Median: ma = 72.62440318352
Median: mb = 61.29443716829
Median: mc = 42.5

Inradius: r = 17
Circumradius: R = 42.5

Vertex coordinates: A[85; 0] B[0; 0] C[30.6; 40.8]
Centroid: CG[38.53333333333; 13.6]
Coordinates of the circumscribed circle: U[42.5; 0]
Coordinates of the inscribed circle: I[34; 17]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 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    