# 27 27 30 triangle

### Acute isosceles triangle.

Sides: a = 27   b = 27   c = 30

Area: T = 336.749916481
Perimeter: p = 84
Semiperimeter: s = 42

Angle ∠ A = α = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 67.49879771918° = 67°29'53″ = 1.17880619404 rad

Height: ha = 24.94443825785
Height: hb = 24.94443825785
Height: hc = 22.45499443206

Median: ma = 25.14545819214
Median: mb = 25.14545819214
Median: mc = 22.45499443206

Inradius: r = 8.01878372574
Circumradius: R = 16.23661204462

Vertex coordinates: A[30; 0] B[0; 0] C[15; 22.45499443206]
Centroid: CG[15; 7.48333147735]
Coordinates of the circumscribed circle: U[15; 6.21438238745]
Coordinates of the inscribed circle: I[15; 8.01878372574]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 112.5022022808° = 112°30'7″ = 1.17880619404 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    