# 16 17 22 triangle

### Acute scalene triangle.

Sides: a = 16   b = 17   c = 22

Area: T = 135.1422286128
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 46.27766909947° = 46°16'36″ = 0.80876806248 rad
Angle ∠ B = β = 50.1621560023° = 50°9'42″ = 0.87554843803 rad
Angle ∠ C = γ = 83.56217489823° = 83°33'42″ = 1.45884276485 rad

Height: ha = 16.8932785766
Height: hb = 15.89990924857
Height: hc = 12.28656623753

Median: ma = 17.95882849961
Median: mb = 17.25554339267
Median: mc = 12.30985336251

Inradius: r = 4.91442649501
Circumradius: R = 11.07698142148

Vertex coordinates: A[22; 0] B[0; 0] C[10.25; 12.28656623753]
Centroid: CG[10.75; 4.09552207918]
Coordinates of the circumscribed circle: U[11; 1.24112843145]
Coordinates of the inscribed circle: I[10.5; 4.91442649501]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.7233309005° = 133°43'24″ = 0.80876806248 rad
∠ B' = β' = 129.8388439977° = 129°50'18″ = 0.87554843803 rad
∠ C' = γ' = 96.43882510177° = 96°26'18″ = 1.45884276485 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    