22 22 26 triangle

Acute isosceles triangle.

Sides: a = 22   b = 22   c = 26

Area: T = 230.7277111541
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 53.77884533802° = 53°46'42″ = 0.93986110781 rad
Angle ∠ B = β = 53.77884533802° = 53°46'42″ = 0.93986110781 rad
Angle ∠ C = γ = 72.44330932397° = 72°26'35″ = 1.26443704974 rad

Height: ha = 20.97551919583
Height: hb = 20.97551919583
Height: hc = 17.74882393493

Median: ma = 21.42442852856
Median: mb = 21.42442852856
Median: mc = 17.74882393493

Inradius: r = 6.59222031869
Circumradius: R = 13.63551553096

Vertex coordinates: A[26; 0] B[0; 0] C[13; 17.74882393493]
Centroid: CG[13; 5.91660797831]
Coordinates of the circumscribed circle: U[13; 4.11330840397]
Coordinates of the inscribed circle: I[13; 6.59222031869]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.222154662° = 126°13'18″ = 0.93986110781 rad
∠ B' = β' = 126.222154662° = 126°13'18″ = 0.93986110781 rad
∠ C' = γ' = 107.557690676° = 107°33'25″ = 1.26443704974 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 = 22 ; ; c = 26 ; ;

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

p = a+b+c = 22+22+26 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-22)(35-22)(35-26) } ; ; T = sqrt{ 53235 } = 230.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 230.73 }{ 22 } = 20.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 230.73 }{ 22 } = 20.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 230.73 }{ 26 } = 17.75 ; ;

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**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 53° 46'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 53° 46'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 72° 26'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 230.73 }{ 35 } = 6.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 53° 46'42" } = 13.64 ; ;




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