23 26 28 triangle

Acute scalene triangle.

Sides: a = 23   b = 26   c = 28

Area: T = 279.8633247855
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 50.251118676° = 50°15'4″ = 0.8777048662 rad
Angle ∠ B = β = 60.35989156325° = 60°21'32″ = 1.05334618107 rad
Angle ∠ C = γ = 69.39898976075° = 69°23'24″ = 1.21110821809 rad

Height: ha = 24.33659345961
Height: hb = 21.52879421427
Height: hc = 19.99902319896

Median: ma = 24.44989263568
Median: mb = 22.07994021658
Median: mc = 20.16218451537

Inradius: r = 7.2699175269
Circumradius: R = 14.95773051556

Vertex coordinates: A[28; 0] B[0; 0] C[11.375; 19.99902319896]
Centroid: CG[13.125; 6.66334106632]
Coordinates of the circumscribed circle: U[14; 5.26550714636]
Coordinates of the inscribed circle: I[12.5; 7.2699175269]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.749881324° = 129°44'56″ = 0.8777048662 rad
∠ B' = β' = 119.6411084367° = 119°38'28″ = 1.05334618107 rad
∠ C' = γ' = 110.6110102393° = 110°36'36″ = 1.21110821809 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 = 23 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 23+26+28 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-23)(38.5-26)(38.5-28) } ; ; T = sqrt{ 78323.44 } = 279.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 279.86 }{ 23 } = 24.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 279.86 }{ 26 } = 21.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 279.86 }{ 28 } = 19.99 ; ;

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{ 23**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 50° 15'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 60° 21'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-23**2-26**2 }{ 2 * 26 * 23 } ) = 69° 23'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 279.86 }{ 38.5 } = 7.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 50° 15'4" } = 14.96 ; ;




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