# 13 17 17 triangle

### Acute isosceles triangle.

Sides: a = 13   b = 17   c = 17

Area: T = 102.1043807471
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 44.95990112188° = 44°57'32″ = 0.78546827742 rad
Angle ∠ B = β = 67.52204943906° = 67°31'14″ = 1.17884549397 rad
Angle ∠ C = γ = 67.52204943906° = 67°31'14″ = 1.17884549397 rad

Height: ha = 15.70882780724
Height: hb = 12.01222126436
Height: hc = 12.01222126436

Median: ma = 15.70882780724
Median: mb = 12.52199840255
Median: mc = 12.52199840255

Inradius: r = 4.34548428711
Circumradius: R = 9.19989713534

Vertex coordinates: A[17; 0] B[0; 0] C[4.97105882353; 12.01222126436]
Centroid: CG[7.32435294118; 4.00440708812]
Coordinates of the circumscribed circle: U[8.5; 3.51772537528]
Coordinates of the inscribed circle: I[6.5; 4.34548428711]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0410988781° = 135°2'28″ = 0.78546827742 rad
∠ B' = β' = 112.4879505609° = 112°28'46″ = 1.17884549397 rad
∠ C' = γ' = 112.4879505609° = 112°28'46″ = 1.17884549397 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    