# 5 23 27 triangle

### Obtuse scalene triangle.

Sides: a = 5   b = 23   c = 27

Area: T = 37.31220288915
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 6.90217733189° = 6°54'6″ = 0.12204586686 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 139.5410916919° = 139°32'27″ = 2.43554484415 rad

Height: ha = 14.92548115566
Height: hb = 3.24545242514
Height: hc = 2.7643853992

Median: ma = 24.95549594269
Median: mb = 15.64444878472
Median: mc = 9.7343961167

Inradius: r = 1.35768010506
Circumradius: R = 20.80442827759

Vertex coordinates: A[27; 0] B[0; 0] C[4.16766666667; 2.7643853992]
Centroid: CG[10.38988888889; 0.9211284664]
Coordinates of the circumscribed circle: U[13.5; -15.82993455903]
Coordinates of the inscribed circle: I[4.5; 1.35768010506]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.0988226681° = 173°5'54″ = 0.12204586686 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 40.45990830808° = 40°27'33″ = 2.43554484415 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    