# 13 16 18 triangle

### Acute scalene triangle.

Sides: a = 13   b = 16   c = 18

Area: T = 100.8888242625
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 44.47661894092° = 44°28'34″ = 0.77662559439 rad
Angle ∠ B = β = 59.57549868512° = 59°34'30″ = 1.04397796724 rad
Angle ∠ C = γ = 75.94988237396° = 75°56'56″ = 1.32655570373 rad

Height: ha = 15.52112680962
Height: hb = 12.61110303281
Height: hc = 11.21098047361

Median: ma = 15.74400762387
Median: mb = 13.50992560861
Median: mc = 11.46773449412

Inradius: r = 4.29331167075
Circumradius: R = 9.27875924691

Vertex coordinates: A[18; 0] B[0; 0] C[6.58333333333; 11.21098047361]
Centroid: CG[8.19444444444; 3.73766015787]
Coordinates of the circumscribed circle: U[9; 2.25224924024]
Coordinates of the inscribed circle: I[7.5; 4.29331167075]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5243810591° = 135°31'26″ = 0.77662559439 rad
∠ B' = β' = 120.4255013149° = 120°25'30″ = 1.04397796724 rad
∠ C' = γ' = 104.051117626° = 104°3'4″ = 1.32655570373 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    