# 21 23 26 triangle

### Acute scalene triangle.

Sides: a = 21   b = 23   c = 26

Area: T = 230.0433474152
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 50.29879022662° = 50°17'52″ = 0.87878640014 rad
Angle ∠ B = β = 57.42110296072° = 57°25'16″ = 1.00221860265 rad
Angle ∠ C = γ = 72.28110681266° = 72°16'52″ = 1.26215426257 rad

Height: ha = 21.90989023002
Height: hb = 20.00437803611
Height: hc = 17.69656518579

Median: ma = 22.18767077323
Median: mb = 20.64658228221
Median: mc = 17.77663888346

Inradius: r = 6.57326706901
Circumradius: R = 13.64774203912

Vertex coordinates: A[26; 0] B[0; 0] C[11.30876923077; 17.69656518579]
Centroid: CG[12.43658974359; 5.89985506193]
Coordinates of the circumscribed circle: U[13; 4.15435627277]
Coordinates of the inscribed circle: I[12; 6.57326706901]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.7022097734° = 129°42'8″ = 0.87878640014 rad
∠ B' = β' = 122.5798970393° = 122°34'44″ = 1.00221860265 rad
∠ C' = γ' = 107.7198931873° = 107°43'8″ = 1.26215426257 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    