# 10 23 25 triangle

### Acute scalene triangle.

Sides: a = 10   b = 23   c = 25

Area: T = 114.9965652092
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 23.577723306° = 23°34'38″ = 0.41215003454 rad
Angle ∠ B = β = 66.92109973887° = 66°55'16″ = 1.16879917432 rad
Angle ∠ C = γ = 89.50217695513° = 89°30'6″ = 1.5622100565 rad

Height: ha = 22.99991304183
Height: hb = 10.999621921
Height: hc = 9.21996521673

Median: ma = 23.49546802489
Median: mb = 15.17439909055
Median: mc = 12.58797456254

Inradius: r = 3.96553673135
Circumradius: R = 12.55004726166

Vertex coordinates: A[25; 0] B[0; 0] C[3.92; 9.21996521673]
Centroid: CG[9.64; 3.06765507224]
Coordinates of the circumscribed circle: U[12.5; 0.10986997619]
Coordinates of the inscribed circle: I[6; 3.96553673135]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.423276694° = 156°25'22″ = 0.41215003454 rad
∠ B' = β' = 113.0799002611° = 113°4'44″ = 1.16879917432 rad
∠ C' = γ' = 90.49882304487° = 90°29'54″ = 1.5622100565 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    