# 13 20 21 triangle

### Acute scalene triangle.

Sides: a = 13   b = 20   c = 21

Area: T = 126
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 75.75499673022° = 75°45' = 1.32220863377 rad

Height: ha = 19.38546153846
Height: hb = 12.6
Height: hc = 12

Median: ma = 19.44986503388
Median: mb = 14.31878210633
Median: mc = 13.22003787824

Inradius: r = 4.66766666667
Circumradius: R = 10.83333333333

Vertex coordinates: A[21; 0] B[0; 0] C[5; 12]
Centroid: CG[8.66766666667; 4]
Coordinates of the circumscribed circle: U[10.5; 2.66766666667]
Coordinates of the inscribed circle: I[7; 4.66766666667]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 104.2550032698° = 104°15' = 1.32220863377 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.