# 12 25 26 triangle

### Acute scalene triangle.

Sides: a = 12   b = 25   c = 26

Area: T = 148.1877170497
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 27.12767531173° = 27°7'36″ = 0.47334511573 rad
Angle ∠ B = β = 71.79900431357° = 71°47'24″ = 1.25329726229 rad
Angle ∠ C = γ = 81.0833203747° = 81°5' = 1.41551688735 rad

Height: ha = 24.69878617496
Height: hb = 11.85549736398
Height: hc = 11.39990131152

Median: ma = 24.78991105125
Median: mb = 15.93295323221
Median: mc = 14.68799182559

Inradius: r = 4.7044354619
Circumradius: R = 13.15990338992

Vertex coordinates: A[26; 0] B[0; 0] C[3.75; 11.39990131152]
Centroid: CG[9.91766666667; 3.87996710384]
Coordinates of the circumscribed circle: U[13; 2.04396502544]
Coordinates of the inscribed circle: I[6.5; 4.7044354619]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.8733246883° = 152°52'24″ = 0.47334511573 rad
∠ B' = β' = 108.2109956864° = 108°12'36″ = 1.25329726229 rad
∠ C' = γ' = 98.9176796253° = 98°55' = 1.41551688735 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    