17 22 26 triangle

Acute scalene triangle.

Sides: a = 17   b = 22   c = 26

Area: T = 185.4210973733
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 40.41554390215° = 40°24'56″ = 0.70553824796 rad
Angle ∠ B = β = 57.03656126762° = 57°2'8″ = 0.99554592321 rad
Angle ∠ C = γ = 82.54989483023° = 82°32'56″ = 1.44107509419 rad

Height: ha = 21.81442322039
Height: hb = 16.85664521575
Height: hc = 14.26331518256

Median: ma = 22.53333086785
Median: mb = 19.01331533418
Median: mc = 14.74878812038

Inradius: r = 5.70552607302
Circumradius: R = 13.11107066858

Vertex coordinates: A[26; 0] B[0; 0] C[9.25; 14.26331518256]
Centroid: CG[11.75; 4.75443839419]
Coordinates of the circumscribed circle: U[13; 1.77001852253]
Coordinates of the inscribed circle: I[10.5; 5.70552607302]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.5854560979° = 139°35'4″ = 0.70553824796 rad
∠ B' = β' = 122.9644387324° = 122°57'52″ = 0.99554592321 rad
∠ C' = γ' = 97.45110516977° = 97°27'4″ = 1.44107509419 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 = 22 ; ; c = 26 ; ;

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

p = a+b+c = 17+22+26 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-17)(32.5-22)(32.5-26) } ; ; T = sqrt{ 34380.94 } = 185.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 185.42 }{ 17 } = 21.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 185.42 }{ 22 } = 16.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 185.42 }{ 26 } = 14.26 ; ;

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**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 40° 24'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 57° 2'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-22**2 }{ 2 * 22 * 17 } ) = 82° 32'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 185.42 }{ 32.5 } = 5.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 40° 24'56" } = 13.11 ; ;




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