# 12 15 17 triangle

### Acute scalene triangle.

Sides: a = 12   b = 15   c = 17

Area: T = 87.75496438739
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 43.4990358347° = 43°29'25″ = 0.7599049946 rad
Angle ∠ B = β = 59.34992300599° = 59°20'57″ = 1.03658394731 rad
Angle ∠ C = γ = 77.16604115931° = 77°9'37″ = 1.34767032345 rad

Height: ha = 14.62549406457
Height: hb = 11.76999525165
Height: hc = 10.32334875146

Median: ma = 14.86660687473
Median: mb = 12.65989889012
Median: mc = 10.59548100502

Inradius: r = 3.98986201761
Circumradius: R = 8.71879840992

Vertex coordinates: A[17; 0] B[0; 0] C[6.11876470588; 10.32334875146]
Centroid: CG[7.70658823529; 3.44111625049]
Coordinates of the circumscribed circle: U[8.5; 1.93773297998]
Coordinates of the inscribed circle: I[7; 3.98986201761]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.5109641653° = 136°30'35″ = 0.7599049946 rad
∠ B' = β' = 120.651076994° = 120°39'3″ = 1.03658394731 rad
∠ C' = γ' = 102.8439588407° = 102°50'23″ = 1.34767032345 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    