# 25 27 29 triangle

### Acute scalene triangle.

Sides: a = 25   b = 27   c = 29

Area: T = 312.1832939156
Perimeter: p = 81
Semiperimeter: s = 40.5

Angle ∠ A = α = 52.88327365328° = 52°52'58″ = 0.923297787 rad
Angle ∠ B = β = 59.4510946125° = 59°27'3″ = 1.03876147533 rad
Angle ∠ C = γ = 67.66663173422° = 67°39'59″ = 1.18110000303 rad

Height: ha = 24.97546351325
Height: hb = 23.12546621597
Height: hc = 21.53298578728

Median: ma = 25.07548878362
Median: mb = 23.46880634054
Median: mc = 21.60443977005

Inradius: r = 7.70882207199
Circumradius: R = 15.67659046898

Vertex coordinates: A[29; 0] B[0; 0] C[12.70768965517; 21.53298578728]
Centroid: CG[13.90222988506; 7.17766192909]
Coordinates of the circumscribed circle: U[14.5; 5.95768437821]
Coordinates of the inscribed circle: I[13.5; 7.70882207199]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.1177263467° = 127°7'2″ = 0.923297787 rad
∠ B' = β' = 120.5499053875° = 120°32'57″ = 1.03876147533 rad
∠ C' = γ' = 112.3343682658° = 112°20'1″ = 1.18110000303 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    