# 10 23 27 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 23   c = 27

Area: T = 112.2549721603
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 21.19331307973° = 21°11'35″ = 0.37698899112 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 102.5565857799° = 102°33'21″ = 1.79899373858 rad

Height: ha = 22.45499443206
Height: hb = 9.76108453568
Height: hc = 8.31547941928

Median: ma = 24.57664114549
Median: mb = 16.88002976164
Median: mc = 11.5

Inradius: r = 3.74216573868
Circumradius: R = 13.8310769269

Vertex coordinates: A[27; 0] B[0; 0] C[5.55655555556; 8.31547941928]
Centroid: CG[10.85218518519; 2.77215980643]
Coordinates of the circumscribed circle: U[13.5; -3.00766889715]
Coordinates of the inscribed circle: I[7; 3.74216573868]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.8076869203° = 158°48'25″ = 0.37698899112 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 77.44441422014° = 77°26'39″ = 1.79899373858 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    