# 15 27 27 triangle

### Acute isosceles triangle.

Sides: a = 15   b = 27   c = 27

Area: T = 194.531068524
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 32.25552404263° = 32°15'19″ = 0.56329601465 rad
Angle ∠ B = β = 73.87223797868° = 73°52'21″ = 1.28993162536 rad
Angle ∠ C = γ = 73.87223797868° = 73°52'21″ = 1.28993162536 rad

Height: ha = 25.93774246987
Height: hb = 14.41096803882
Height: hc = 14.41096803882

Median: ma = 25.93774246987
Median: mb = 17.16882847134
Median: mc = 17.16882847134

Inradius: r = 5.63985705867
Circumradius: R = 14.05330528468

Vertex coordinates: A[27; 0] B[0; 0] C[4.16766666667; 14.41096803882]
Centroid: CG[10.38988888889; 4.80332267961]
Coordinates of the circumscribed circle: U[13.5; 3.90436257908]
Coordinates of the inscribed circle: I[7.5; 5.63985705867]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.7454759574° = 147°44'41″ = 0.56329601465 rad
∠ B' = β' = 106.1287620213° = 106°7'39″ = 1.28993162536 rad
∠ C' = γ' = 106.1287620213° = 106°7'39″ = 1.28993162536 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    