# 17 19 20 triangle

### Acute scalene triangle.

Sides: a = 17   b = 19   c = 20

Area: T = 148.9166083752
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 51.60769559808° = 51°36'25″ = 0.90107112988 rad
Angle ∠ B = β = 61.16108105994° = 61°9'39″ = 1.06774575181 rad
Angle ∠ C = γ = 67.23222334198° = 67°13'56″ = 1.17334238366 rad

Height: ha = 17.52195392649
Height: hb = 15.6755377237
Height: hc = 14.89216083752

Median: ma = 17.55770498661
Median: mb = 15.94552187191
Median: mc = 15

Inradius: r = 5.31884315626
Circumradius: R = 10.84550340575

Vertex coordinates: A[20; 0] B[0; 0] C[8.2; 14.89216083752]
Centroid: CG[9.4; 4.96438694584]
Coordinates of the circumscribed circle: U[10; 4.19769946043]
Coordinates of the inscribed circle: I[9; 5.31884315626]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.3933044019° = 128°23'35″ = 0.90107112988 rad
∠ B' = β' = 118.8399189401° = 118°50'21″ = 1.06774575181 rad
∠ C' = γ' = 112.768776658° = 112°46'4″ = 1.17334238366 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    