10 22 26 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 22   c = 26

Area: T = 107.5698582774
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 22.09331769923° = 22°5'35″ = 0.38655986807 rad
Angle ∠ B = β = 55.83877404834° = 55°50'16″ = 0.97545524183 rad
Angle ∠ C = γ = 102.0699082524° = 102°4'9″ = 1.78114415545 rad

Height: ha = 21.51437165548
Height: hb = 9.77989620704
Height: hc = 8.27545063672

Median: ma = 23.55884379788
Median: mb = 16.34401346384
Median: mc = 11.09105365064

Inradius: r = 3.7099261475
Circumradius: R = 13.2943844384

Vertex coordinates: A[26; 0] B[0; 0] C[5.61553846154; 8.27545063672]
Centroid: CG[10.53884615385; 2.75881687891]
Coordinates of the circumscribed circle: U[13; -2.78796220076]
Coordinates of the inscribed circle: I[7; 3.7099261475]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.9076823008° = 157°54'25″ = 0.38655986807 rad
∠ B' = β' = 124.1622259517° = 124°9'44″ = 0.97545524183 rad
∠ C' = γ' = 77.93109174756° = 77°55'51″ = 1.78114415545 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 = 10 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 10+22+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-10)(29-22)(29-26) } ; ; T = sqrt{ 11571 } = 107.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.57 }{ 10 } = 21.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.57 }{ 22 } = 9.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.57 }{ 26 } = 8.27 ; ;

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{ 10**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 22° 5'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 55° 50'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-22**2 }{ 2 * 22 * 10 } ) = 102° 4'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.57 }{ 29 } = 3.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 22° 5'35" } = 13.29 ; ;




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