9 24 26 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 24   c = 26

Area: T = 107.8955493418
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 20.23217918143° = 20°13'54″ = 0.35331113807 rad
Angle ∠ B = β = 67.24774417914° = 67°14'51″ = 1.17436892728 rad
Angle ∠ C = γ = 92.52107663943° = 92°31'15″ = 1.6154792 rad

Height: ha = 23.97767763152
Height: hb = 8.99112911182
Height: hc = 8.32996533399

Median: ma = 24.61219889485
Median: mb = 15.31333928311
Median: mc = 12.62993309403

Inradius: r = 3.65774743532
Circumradius: R = 13.01325916803

Vertex coordinates: A[26; 0] B[0; 0] C[3.48107692308; 8.32996533399]
Centroid: CG[9.82769230769; 2.76765511133]
Coordinates of the circumscribed circle: U[13; -0.572231306]
Coordinates of the inscribed circle: I[5.5; 3.65774743532]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.7688208186° = 159°46'6″ = 0.35331113807 rad
∠ B' = β' = 112.7532558209° = 112°45'9″ = 1.17436892728 rad
∠ C' = γ' = 87.47992336057° = 87°28'45″ = 1.6154792 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 = 24 ; ; c = 26 ; ;

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

p = a+b+c = 9+24+26 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-9)(29.5-24)(29.5-26) } ; ; T = sqrt{ 11641.44 } = 107.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.9 }{ 9 } = 23.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.9 }{ 24 } = 8.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.9 }{ 26 } = 8.3 ; ;

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**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 20° 13'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-9**2-26**2 }{ 2 * 9 * 26 } ) = 67° 14'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-9**2-24**2 }{ 2 * 24 * 9 } ) = 92° 31'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.9 }{ 29.5 } = 3.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 20° 13'54" } = 13.01 ; ;




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