# 12 12 15 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 12   c = 15

Area: T = 70.2566227482
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ B = β = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ C = γ = 77.3644374907° = 77°21'52″ = 1.35502630659 rad

Height: ha = 11.7099371247
Height: hb = 11.7099371247
Height: hc = 9.36774969976

Median: ma = 12.1866057607
Median: mb = 12.1866057607
Median: mc = 9.36774969976

Inradius: r = 3.60328834606
Circumradius: R = 7.68661513826

Vertex coordinates: A[15; 0] B[0; 0] C[7.5; 9.36774969976]
Centroid: CG[7.5; 3.12224989992]
Coordinates of the circumscribed circle: U[7.5; 1.6811345615]
Coordinates of the inscribed circle: I[7.5; 3.60328834606]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ B' = β' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ C' = γ' = 102.6365625093° = 102°38'8″ = 1.35502630659 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 ### 6. Inradius ### 7. Circumradius ### 8. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.