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

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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.

a = 10 ; ; b = 23 ; ; c = 25 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 10+23+25 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-10)(29-23)(29-25) } ; ; T = sqrt{ 13224 } = 115 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115 }{ 10 } = 23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115 }{ 23 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115 }{ 25 } = 9.2 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 10**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 23° 34'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-10**2-25**2 }{ 2 * 10 * 25 } ) = 66° 55'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-10**2-23**2 }{ 2 * 23 * 10 } ) = 89° 30'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115 }{ 29 } = 3.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 23° 34'38" } = 12.5 ; ;




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