# 27 29 29 triangle

### Acute isosceles triangle.

Sides: a = 27   b = 29   c = 29

Area: T = 346.4932694728
Perimeter: p = 85
Semiperimeter: s = 42.5

Angle ∠ A = α = 55.4877404317° = 55°29'15″ = 0.96884378987 rad
Angle ∠ B = β = 62.25662978415° = 62°15'23″ = 1.08765773774 rad
Angle ∠ C = γ = 62.25662978415° = 62°15'23″ = 1.08765773774 rad

Height: ha = 25.66661255354
Height: hb = 23.89660479123
Height: hc = 23.89660479123

Median: ma = 25.66661255354
Median: mb = 23.97439441895
Median: mc = 23.97439441895

Inradius: r = 8.15327692877
Circumradius: R = 16.38334622962

Vertex coordinates: A[29; 0] B[0; 0] C[12.56989655172; 23.89660479123]
Centroid: CG[13.85663218391; 7.96553493041]
Coordinates of the circumscribed circle: U[14.5; 7.62767841724]
Coordinates of the inscribed circle: I[13.5; 8.15327692877]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.5132595683° = 124°30'45″ = 0.96884378987 rad
∠ B' = β' = 117.7443702158° = 117°44'37″ = 1.08765773774 rad
∠ C' = γ' = 117.7443702158° = 117°44'37″ = 1.08765773774 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    