# 13 21 21 triangle

### Acute isosceles triangle.

Sides: a = 13   b = 21   c = 21

Area: T = 129.797671606
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 36.06110707867° = 36°3'40″ = 0.6299384417 rad
Angle ∠ B = β = 71.96994646067° = 71°58'10″ = 1.25661041183 rad
Angle ∠ C = γ = 71.96994646067° = 71°58'10″ = 1.25661041183 rad

Height: ha = 19.96987255477
Height: hb = 12.36215920057
Height: hc = 12.36215920057

Median: ma = 19.96987255477
Median: mb = 13.9555285737
Median: mc = 13.9555285737

Inradius: r = 4.7219880584
Circumradius: R = 11.04222670427

Vertex coordinates: A[21; 0] B[0; 0] C[4.02438095238; 12.36215920057]
Centroid: CG[8.34112698413; 4.12105306686]
Coordinates of the circumscribed circle: U[10.5; 3.41878445608]
Coordinates of the inscribed circle: I[6.5; 4.7219880584]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.9398929213° = 143°56'20″ = 0.6299384417 rad
∠ B' = β' = 108.0310535393° = 108°1'50″ = 1.25661041183 rad
∠ C' = γ' = 108.0310535393° = 108°1'50″ = 1.25661041183 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 ### 6. Inradius ### 7. Circumradius ### 8. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.