# 15 20 20 triangle

### Acute isosceles triangle.

Sides: a = 15   b = 20   c = 20

Area: T = 139.0543721633
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 67.9765687163° = 67°58'32″ = 1.18663995523 rad

Height: ha = 18.54404962177
Height: hb = 13.90553721633
Height: hc = 13.90553721633

Median: ma = 18.54404962177
Median: mb = 14.57773797371
Median: mc = 14.57773797371

Inradius: r = 5.05664989685
Circumradius: R = 10.78771977994

Vertex coordinates: A[20; 0] B[0; 0] C[5.625; 13.90553721633]
Centroid: CG[8.54216666667; 4.63551240544]
Coordinates of the circumscribed circle: U[10; 4.04551991748]
Coordinates of the inscribed circle: I[7.5; 5.05664989685]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 112.0244312837° = 112°1'28″ = 1.18663995523 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    