# 15 27 30 triangle

### Acute scalene triangle.

Sides: a = 15   b = 27   c = 30

Area: T = 202.0499498886
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ B = β = 63.89661188627° = 63°53'46″ = 1.11551976534 rad
Angle ∠ C = γ = 86.17774462707° = 86°10'39″ = 1.50440801784 rad

Height: ha = 26.94399331848
Height: hb = 14.96766295471
Height: hc = 13.47699665924

Median: ma = 27.5366339626
Median: mb = 19.5
Median: mc = 15.87545078664

Inradius: r = 5.61224860802
Circumradius: R = 15.03334448576

Vertex coordinates: A[30; 0] B[0; 0] C[6.6; 13.47699665924]
Centroid: CG[12.2; 4.49899888641]
Coordinates of the circumscribed circle: U[15; 1.00222296572]
Coordinates of the inscribed circle: I[9; 5.61224860802]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ B' = β' = 116.1043881137° = 116°6'14″ = 1.11551976534 rad
∠ C' = γ' = 93.82325537293° = 93°49'21″ = 1.50440801784 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    