9 25 26 triangle

Acute scalene triangle.

Sides: a = 9   b = 25   c = 26

Area: T = 112.2549721603
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 20.20552235834° = 20°12'19″ = 0.35326476776 rad
Angle ∠ B = β = 73.61773301459° = 73°37'2″ = 1.28548647976 rad
Angle ∠ C = γ = 86.17774462707° = 86°10'39″ = 1.50440801784 rad

Height: ha = 24.94443825785
Height: hb = 8.98799777283
Height: hc = 8.63545939695

Median: ma = 25.10547804213
Median: mb = 14.90880515159
Median: mc = 13.56546599663

Inradius: r = 3.74216573868
Circumradius: R = 13.02989855432

Vertex coordinates: A[26; 0] B[0; 0] C[2.53884615385; 8.63545939695]
Centroid: CG[9.51328205128; 2.87881979898]
Coordinates of the circumscribed circle: U[13; 0.86985990362]
Coordinates of the inscribed circle: I[5; 3.74216573868]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.7954776417° = 159°47'41″ = 0.35326476776 rad
∠ B' = β' = 106.3832669854° = 106°22'58″ = 1.28548647976 rad
∠ C' = γ' = 93.82325537293° = 93°49'21″ = 1.50440801784 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 = 9 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 9+25+26 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-9)(30-25)(30-26) } ; ; T = sqrt{ 12600 } = 112.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 112.25 }{ 9 } = 24.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 112.25 }{ 25 } = 8.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 112.25 }{ 26 } = 8.63 ; ;

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{ 9**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 20° 12'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-9**2-26**2 }{ 2 * 9 * 26 } ) = 73° 37'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-9**2-25**2 }{ 2 * 25 * 9 } ) = 86° 10'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 112.25 }{ 30 } = 3.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 20° 12'19" } = 13.03 ; ;




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