# 13 18 21 triangle

### Acute scalene triangle.

Sides: a = 13   b = 18   c = 21

Area: T = 116.276553483
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 37.96875057136° = 37°58'3″ = 0.66326579835 rad
Angle ∠ B = β = 58.41218644948° = 58°24'43″ = 1.01994793577 rad
Angle ∠ C = γ = 83.62106297916° = 83°37'14″ = 1.45994553125 rad

Height: ha = 17.889854382
Height: hb = 12.921950387
Height: hc = 11.074386046

Median: ma = 18.44658667457
Median: mb = 14.96766295471
Median: mc = 11.67326175299

Inradius: r = 4.4722135955
Circumradius: R = 10.56554211937

Vertex coordinates: A[21; 0] B[0; 0] C[6.81095238095; 11.074386046]
Centroid: CG[9.27698412698; 3.691128682]
Coordinates of the circumscribed circle: U[10.5; 1.17439356882]
Coordinates of the inscribed circle: I[8; 4.4722135955]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.0322494286° = 142°1'57″ = 0.66326579835 rad
∠ B' = β' = 121.5888135505° = 121°35'17″ = 1.01994793577 rad
∠ C' = γ' = 96.37993702084° = 96°22'46″ = 1.45994553125 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.