# 12 16 17 triangle

### Acute scalene triangle.

Sides: a = 12   b = 16   c = 17

Area: T = 91.90217818108
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 42.51222944223° = 42°30'44″ = 0.74219795102 rad
Angle ∠ B = β = 64.29895431711° = 64°17'22″ = 1.12220642029 rad
Angle ∠ C = γ = 73.19881624066° = 73°11'53″ = 1.27875489404 rad

Height: ha = 15.31769636351
Height: hb = 11.48877227264
Height: hc = 10.81219743307

Median: ma = 15.37985564992
Median: mb = 12.34990890352
Median: mc = 11.30326545555

Inradius: r = 4.0854523636
Circumradius: R = 8.87990443876

Vertex coordinates: A[17; 0] B[0; 0] C[5.20658823529; 10.81219743307]
Centroid: CG[7.40219607843; 3.60439914436]
Coordinates of the circumscribed circle: U[8.5; 2.56765987683]
Coordinates of the inscribed circle: I[6.5; 4.0854523636]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.4887705578° = 137°29'16″ = 0.74219795102 rad
∠ B' = β' = 115.7110456829° = 115°42'38″ = 1.12220642029 rad
∠ C' = γ' = 106.8021837593° = 106°48'7″ = 1.27875489404 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    