14 23 26 triangle

Acute scalene triangle.

Sides: a = 14   b = 23   c = 26

Area: T = 160.533329094
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 32.47329000805° = 32°28'22″ = 0.56767590241 rad
Angle ∠ B = β = 61.89107787174° = 61°53'27″ = 1.08801978652 rad
Angle ∠ C = γ = 85.63663212021° = 85°38'11″ = 1.49546357643 rad

Height: ha = 22.93333272771
Height: hb = 13.95994166035
Height: hc = 12.34987146877

Median: ma = 23.5276580712
Median: mb = 17.42884250579
Median: mc = 13.91104277432

Inradius: r = 5.09662949505
Circumradius: R = 13.03877941407

Vertex coordinates: A[26; 0] B[0; 0] C[6.59661538462; 12.34987146877]
Centroid: CG[10.86553846154; 4.11662382292]
Coordinates of the circumscribed circle: U[13; 0.99220060759]
Coordinates of the inscribed circle: I[8.5; 5.09662949505]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.5277099919° = 147°31'38″ = 0.56767590241 rad
∠ B' = β' = 118.1099221283° = 118°6'33″ = 1.08801978652 rad
∠ C' = γ' = 94.36436787979° = 94°21'49″ = 1.49546357643 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 = 14 ; ; b = 23 ; ; c = 26 ; ;

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

p = a+b+c = 14+23+26 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-14)(31.5-23)(31.5-26) } ; ; T = sqrt{ 25770.94 } = 160.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 160.53 }{ 14 } = 22.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 160.53 }{ 23 } = 13.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 160.53 }{ 26 } = 12.35 ; ;

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{ 14**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 32° 28'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 61° 53'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-23**2 }{ 2 * 23 * 14 } ) = 85° 38'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 160.53 }{ 31.5 } = 5.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 32° 28'22" } = 13.04 ; ;




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