# 13 14 17 triangle

### Acute scalene triangle.

Sides: a = 13   b = 14   c = 17

Area: T = 88.99443818451
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 48.40546480534° = 48°24'17″ = 0.84548204818 rad
Angle ∠ B = β = 53.64768753478° = 53°38'49″ = 0.93663146082 rad
Angle ∠ C = γ = 77.94884765988° = 77°56'55″ = 1.36604575636 rad

Height: ha = 13.69114433608
Height: hb = 12.71334831207
Height: hc = 10.47699272759

Median: ma = 14.15109716981
Median: mb = 13.4166407865
Median: mc = 10.5

Inradius: r = 4.04551991748
Circumradius: R = 8.69215598936

Vertex coordinates: A[17; 0] B[0; 0] C[7.70658823529; 10.47699272759]
Centroid: CG[8.23552941176; 3.49899757586]
Coordinates of the circumscribed circle: U[8.5; 1.81547212965]
Coordinates of the inscribed circle: I[8; 4.04551991748]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.5955351947° = 131°35'43″ = 0.84548204818 rad
∠ B' = β' = 126.3533124652° = 126°21'11″ = 0.93663146082 rad
∠ C' = γ' = 102.0521523401° = 102°3'5″ = 1.36604575636 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    