# 15 16 27 triangle

### Obtuse scalene triangle.

Sides: a = 15   b = 16   c = 27

Area: T = 102.7422396312
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 28.40222819014° = 28°24'8″ = 0.49657133343 rad
Angle ∠ B = β = 30.48987955881° = 30°29'20″ = 0.5322129868 rad
Angle ∠ C = γ = 121.1098922511° = 121°6'32″ = 2.11437494514 rad

Height: ha = 13.6998986175
Height: hb = 12.8432799539
Height: hc = 7.6110547875

Median: ma = 20.88765985742
Median: mb = 20.32224014329
Median: mc = 7.63221687612

Inradius: r = 3.54328412521
Circumradius: R = 15.76875901881

Vertex coordinates: A[27; 0] B[0; 0] C[12.92659259259; 7.6110547875]
Centroid: CG[13.30986419753; 2.53768492917]
Coordinates of the circumscribed circle: U[13.5; -8.14765882639]
Coordinates of the inscribed circle: I[13; 3.54328412521]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.5987718099° = 151°35'52″ = 0.49657133343 rad
∠ B' = β' = 149.5111204412° = 149°30'40″ = 0.5322129868 rad
∠ C' = γ' = 58.89110774895° = 58°53'28″ = 2.11437494514 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    