# 15 17 18 triangle

### Acute scalene triangle.

Sides: a = 15   b = 17   c = 18

Area: T = 118.3221595662
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 50.6555112747° = 50°39'18″ = 0.88440985004 rad
Angle ∠ B = β = 61.21877953194° = 61°13'4″ = 1.06884520891 rad
Angle ∠ C = γ = 68.12770919336° = 68°7'38″ = 1.18990420641 rad

Height: ha = 15.77662127549
Height: hb = 13.92201877249
Height: hc = 13.14768439624

Median: ma = 15.81992920196
Median: mb = 14.22114626533
Median: mc = 13.26664991614

Inradius: r = 4.73328638265
Circumradius: R = 9.6988145073

Vertex coordinates: A[18; 0] B[0; 0] C[7.22222222222; 13.14768439624]
Centroid: CG[8.40774074074; 4.38222813208]
Coordinates of the circumscribed circle: U[9; 3.6133034439]
Coordinates of the inscribed circle: I[8; 4.73328638265]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.3454887253° = 129°20'42″ = 0.88440985004 rad
∠ B' = β' = 118.7822204681° = 118°46'56″ = 1.06884520891 rad
∠ C' = γ' = 111.8732908066° = 111°52'22″ = 1.18990420641 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    