# 21 24 27 triangle

### Acute scalene triangle.

Sides: a = 21   b = 24   c = 27

Area: T = 241.495534157
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ B = β = 58.41218644948° = 58°24'43″ = 1.01994793577 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

Height: ha = 232.99955634
Height: hb = 20.12546117975
Height: hc = 17.889854382

Median: ma = 23.28662620444
Median: mb = 21
Median: mc = 18.06223918682

Inradius: r = 6.70882039325
Circumradius: R = 14.08772282582

Vertex coordinates: A[27; 0] B[0; 0] C[11; 17.889854382]
Centroid: CG[12.66766666667; 5.963284794]
Coordinates of the circumscribed circle: U[13.5; 4.02549223595]
Coordinates of the inscribed circle: I[12; 6.70882039325]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ B' = β' = 121.5888135505° = 121°35'17″ = 1.01994793577 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 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    