22 23 25 triangle

Acute scalene triangle.

Sides: a = 22   b = 23   c = 25

Area: T = 233.6666428911
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 54.36657656498° = 54°21'57″ = 0.9498861611 rad
Angle ∠ B = β = 58.17986314749° = 58°10'43″ = 1.01554086735 rad
Angle ∠ C = γ = 67.45656028753° = 67°27'20″ = 1.17773223691 rad

Height: ha = 21.24224026283
Height: hb = 20.31988199053
Height: hc = 18.69333143129

Median: ma = 21.35441565041
Median: mb = 20.5498722588
Median: mc = 18.71549672722

Inradius: r = 6.67661836832
Circumradius: R = 13.53442505757

Vertex coordinates: A[25; 0] B[0; 0] C[11.6; 18.69333143129]
Centroid: CG[12.2; 6.2311104771]
Coordinates of the circumscribed circle: U[12.5; 5.18990209717]
Coordinates of the inscribed circle: I[12; 6.67661836832]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.634423435° = 125°38'3″ = 0.9498861611 rad
∠ B' = β' = 121.8211368525° = 121°49'17″ = 1.01554086735 rad
∠ C' = γ' = 112.5444397125° = 112°32'40″ = 1.17773223691 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 = 22 ; ; b = 23 ; ; c = 25 ; ;

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

p = a+b+c = 22+23+25 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-22)(35-23)(35-25) } ; ; T = sqrt{ 54600 } = 233.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 233.67 }{ 22 } = 21.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 233.67 }{ 23 } = 20.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 233.67 }{ 25 } = 18.69 ; ;

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{ 22**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 54° 21'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 58° 10'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-22**2-23**2 }{ 2 * 23 * 22 } ) = 67° 27'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 233.67 }{ 35 } = 6.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 54° 21'57" } = 13.53 ; ;




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