# 18 21 26 triangle

### Acute scalene triangle.

Sides: a = 18   b = 21   c = 26

Area: T = 187.6865741334
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 43.43220282875° = 43°25'55″ = 0.75880318944 rad
Angle ∠ B = β = 53.32987880616° = 53°19'44″ = 0.93107629378 rad
Angle ∠ C = γ = 83.23991836509° = 83°14'21″ = 1.45327978214 rad

Height: ha = 20.85439712593
Height: hb = 17.8754832508
Height: hc = 14.4377364718

Median: ma = 21.85217733834
Median: mb = 19.74220870224
Median: mc = 14.61216391962

Inradius: r = 5.77549458872
Circumradius: R = 13.09110317563

Vertex coordinates: A[26; 0] B[0; 0] C[10.75; 14.4377364718]
Centroid: CG[12.25; 4.8122454906]
Coordinates of the circumscribed circle: U[13; 1.54111399819]
Coordinates of the inscribed circle: I[11.5; 5.77549458872]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.5687971712° = 136°34'5″ = 0.75880318944 rad
∠ B' = β' = 126.6711211938° = 126°40'16″ = 0.93107629378 rad
∠ C' = γ' = 96.76108163491° = 96°45'39″ = 1.45327978214 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    