22 25 26 triangle

Acute scalene triangle.

Sides: a = 22   b = 25   c = 26

Area: T = 252.7988214986
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 51.06332913786° = 51°3'48″ = 0.89112225615 rad
Angle ∠ B = β = 62.11876632793° = 62°7'4″ = 1.08441577479 rad
Angle ∠ C = γ = 66.81990453421° = 66°49'9″ = 1.16662123443 rad

Height: ha = 22.98216559078
Height: hb = 20.22438571989
Height: hc = 19.44660165374

Median: ma = 23.0110866998
Median: mb = 20.58551888502
Median: mc = 19.63441539161

Inradius: r = 6.92659784928
Circumradius: R = 14.14217137783

Vertex coordinates: A[26; 0] B[0; 0] C[10.28884615385; 19.44660165374]
Centroid: CG[12.09661538462; 6.48220055125]
Coordinates of the circumscribed circle: U[13; 5.56766927873]
Coordinates of the inscribed circle: I[11.5; 6.92659784928]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.9376708621° = 128°56'12″ = 0.89112225615 rad
∠ B' = β' = 117.8822336721° = 117°52'56″ = 1.08441577479 rad
∠ C' = γ' = 113.1810954658° = 113°10'51″ = 1.16662123443 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 = 22 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 22+25+26 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-22)(36.5-25)(36.5-26) } ; ; T = sqrt{ 63906.94 } = 252.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 252.8 }{ 22 } = 22.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 252.8 }{ 25 } = 20.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 252.8 }{ 26 } = 19.45 ; ;

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{ 22**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 51° 3'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 62° 7'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-22**2-25**2 }{ 2 * 25 * 22 } ) = 66° 49'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 252.8 }{ 36.5 } = 6.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 51° 3'48" } = 14.14 ; ;




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