# 9 24 27 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 24   c = 27

Area: T = 106.4899436096
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 61.21877953194° = 61°13'4″ = 1.06884520891 rad
Angle ∠ C = γ = 99.59440682269° = 99°35'39″ = 1.7388244406 rad

Height: ha = 23.66443191324
Height: hb = 8.87441196746
Height: hc = 7.88881063775

Median: ma = 25.14545819214
Median: mb = 16.15554944214
Median: mc = 12.09333866224

Inradius: r = 3.55496478699
Circumradius: R = 13.69114989266

Vertex coordinates: A[27; 0] B[0; 0] C[4.33333333333; 7.88881063775]
Centroid: CG[10.44444444444; 2.62993687925]
Coordinates of the circumscribed circle: U[13.5; -2.28219164878]
Coordinates of the inscribed circle: I[6; 3.55496478699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 118.7822204681° = 118°46'56″ = 1.06884520891 rad
∠ C' = γ' = 80.40659317731° = 80°24'21″ = 1.7388244406 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    