# 13 17 21 triangle

### Acute scalene triangle.

Sides: a = 13   b = 17   c = 21

Area: T = 110.4188238983
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ B = β = 53.99110168022° = 53°59'28″ = 0.94223210097 rad
Angle ∠ C = γ = 87.7965772496° = 87°47'45″ = 1.53223252994 rad

Height: ha = 16.98774213819
Height: hb = 12.99903810568
Height: hc = 10.51660227602

Median: ma = 17.96552442232
Median: mb = 15.25661463024
Median: mc = 10.89772473589

Inradius: r = 4.33301270189
Circumradius: R = 10.50877748993

Vertex coordinates: A[21; 0] B[0; 0] C[7.64328571429; 10.51660227602]
Centroid: CG[9.54876190476; 3.50553409201]
Coordinates of the circumscribed circle: U[10.5; 0.40441451884]
Coordinates of the inscribed circle: I[8.5; 4.33301270189]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ B' = β' = 126.0098983198° = 126°32″ = 0.94223210097 rad
∠ C' = γ' = 92.2044227504° = 92°12'15″ = 1.53223252994 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    