# 11 17 18 triangle

### Acute scalene triangle.

Sides: a = 11   b = 17   c = 18

Area: T = 90.99545053286
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 36.49437665998° = 36°29'38″ = 0.63769363836 rad
Angle ∠ B = β = 66.88001568171° = 66°48'1″ = 1.16658826773 rad
Angle ∠ C = γ = 76.70660765831° = 76°42'22″ = 1.33987735927 rad

Height: ha = 16.54444555143
Height: hb = 10.7055235921
Height: hc = 10.11105005921

Median: ma = 16.62107701386
Median: mb = 12.25876506721
Median: mc = 11.13655287257

Inradius: r = 3.95662828404
Circumradius: R = 9.24878111394

Vertex coordinates: A[18; 0] B[0; 0] C[4.33333333333; 10.11105005921]
Centroid: CG[7.44444444444; 3.3770166864]
Coordinates of the circumscribed circle: U[9; 2.12765020267]
Coordinates of the inscribed circle: I[6; 3.95662828404]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.50662334° = 143°30'22″ = 0.63769363836 rad
∠ B' = β' = 113.2199843183° = 113°11'59″ = 1.16658826773 rad
∠ C' = γ' = 103.2943923417° = 103°17'38″ = 1.33987735927 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    