# 12 15 15 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 15   c = 15

Area: T = 82.48663625092
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 47.15663569564° = 47°9'23″ = 0.82330336921 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 66.42218215218° = 66°25'19″ = 1.15992794807 rad

Height: ha = 13.74877270849
Height: hb = 10.99881816679
Height: hc = 10.99881816679

Median: ma = 13.74877270849
Median: mb = 11.32547516529
Median: mc = 11.32547516529

Inradius: r = 3.92879220242
Circumradius: R = 8.18331708838

Vertex coordinates: A[15; 0] B[0; 0] C[4.8; 10.99881816679]
Centroid: CG[6.6; 3.6666060556]
Coordinates of the circumscribed circle: U[7.5; 3.27332683535]
Coordinates of the inscribed circle: I[6; 3.92879220242]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.8443643044° = 132°50'37″ = 0.82330336921 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad
∠ C' = γ' = 113.5788178478° = 113°34'41″ = 1.15992794807 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.