17 24 26 triangle

Acute scalene triangle.

Sides: a = 17   b = 24   c = 26

Area: T = 198.4532607693
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 39.49990963429° = 39°29'57″ = 0.68993892827 rad
Angle ∠ B = β = 63.89332317717° = 63°53'36″ = 1.11551472642 rad
Angle ∠ C = γ = 76.60876718853° = 76°36'28″ = 1.33770561067 rad

Height: ha = 23.34773656109
Height: hb = 16.53877173077
Height: hc = 15.26655852071

Median: ma = 23.53218932515
Median: mb = 18.3988369493
Median: mc = 16.23326830807

Inradius: r = 5.92439584386
Circumradius: R = 13.36333920503

Vertex coordinates: A[26; 0] B[0; 0] C[7.48107692308; 15.26655852071]
Centroid: CG[11.16602564103; 5.08985284024]
Coordinates of the circumscribed circle: U[13; 3.09551974234]
Coordinates of the inscribed circle: I[9.5; 5.92439584386]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.5010903657° = 140°30'3″ = 0.68993892827 rad
∠ B' = β' = 116.1076768228° = 116°6'24″ = 1.11551472642 rad
∠ C' = γ' = 103.3922328115° = 103°23'32″ = 1.33770561067 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 = 17 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 17+24+26 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-17)(33.5-24)(33.5-26) } ; ; T = sqrt{ 39383.44 } = 198.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 198.45 }{ 17 } = 23.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 198.45 }{ 24 } = 16.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 198.45 }{ 26 } = 15.27 ; ;

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{ 17**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 39° 29'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 63° 53'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-24**2 }{ 2 * 24 * 17 } ) = 76° 36'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 198.45 }{ 33.5 } = 5.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 39° 29'57" } = 13.36 ; ;




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