# 10 12 17 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 12   c = 17

Area: T = 58.93658761706
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 35.2966144734° = 35°17'46″ = 0.61660339389 rad
Angle ∠ B = β = 43.89769323912° = 43°53'49″ = 0.76661460018 rad
Angle ∠ C = γ = 100.8076922875° = 100°48'25″ = 1.7599412713 rad

Height: ha = 11.78771752341
Height: hb = 9.82326460284
Height: hc = 6.93436324907

Median: ma = 13.83883525031
Median: mb = 12.5989678312
Median: mc = 7.05333679898

Inradius: r = 3.02223526241
Circumradius: R = 8.65334727765

Vertex coordinates: A[17; 0] B[0; 0] C[7.20658823529; 6.93436324907]
Centroid: CG[8.0698627451; 2.31112108302]
Coordinates of the circumscribed circle: U[8.5; -1.62325261456]
Coordinates of the inscribed circle: I[7.5; 3.02223526241]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.7043855266° = 144°42'14″ = 0.61660339389 rad
∠ B' = β' = 136.1033067609° = 136°6'11″ = 0.76661460018 rad
∠ C' = γ' = 79.19330771251° = 79°11'35″ = 1.7599412713 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    