# 13 29 30 triangle

### Acute scalene triangle.

Sides: a = 13   b = 29   c = 30

Area: T = 186.4833243215
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 25.38549039049° = 25°23'6″ = 0.44330501534 rad
Angle ∠ B = β = 73.00438351829° = 73°14″ = 1.27441572905 rad
Angle ∠ C = γ = 81.61112609121° = 81°36'41″ = 1.42443852096 rad

Height: ha = 28.69897297254
Height: hb = 12.86109133252
Height: hc = 12.43222162143

Median: ma = 28.77993328623
Median: mb = 18.00769431054
Median: mc = 16.73332005307

Inradius: r = 5.18800900893
Circumradius: R = 15.16222202148

Vertex coordinates: A[30; 0] B[0; 0] C[3.8; 12.43222162143]
Centroid: CG[11.26766666667; 4.14440720714]
Coordinates of the circumscribed circle: U[15; 2.21219949916]
Coordinates of the inscribed circle: I[7; 5.18800900893]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.6155096095° = 154°36'54″ = 0.44330501534 rad
∠ B' = β' = 106.9966164817° = 106°59'46″ = 1.27441572905 rad
∠ C' = γ' = 98.38987390879° = 98°23'19″ = 1.42443852096 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    