16 22 26 triangle

Acute scalene triangle.

Sides: a = 16   b = 22   c = 26

Area: T = 175.2711218402
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 37.79548789633° = 37°47'42″ = 0.66596450783 rad
Angle ∠ B = β = 57.42110296072° = 57°25'16″ = 1.00221860265 rad
Angle ∠ C = γ = 84.78440914295° = 84°47'3″ = 1.48797615488 rad

Height: ha = 21.90989023002
Height: hb = 15.93437471274
Height: hc = 13.48224014155

Median: ma = 22.71656333832
Median: mb = 18.5744175621
Median: mc = 14.17774468788

Inradius: r = 5.47772255751
Circumradius: R = 13.05440542872

Vertex coordinates: A[26; 0] B[0; 0] C[8.61553846154; 13.48224014155]
Centroid: CG[11.53884615385; 4.49441338052]
Coordinates of the circumscribed circle: U[13; 1.18767322079]
Coordinates of the inscribed circle: I[10; 5.47772255751]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.2055121037° = 142°12'18″ = 0.66596450783 rad
∠ B' = β' = 122.5798970393° = 122°34'44″ = 1.00221860265 rad
∠ C' = γ' = 95.21659085705° = 95°12'57″ = 1.48797615488 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 = 16 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 16+22+26 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-16)(32-22)(32-26) } ; ; T = sqrt{ 30720 } = 175.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 175.27 }{ 16 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 175.27 }{ 22 } = 15.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 175.27 }{ 26 } = 13.48 ; ;

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{ 16**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 37° 47'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 57° 25'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-22**2 }{ 2 * 22 * 16 } ) = 84° 47'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 175.27 }{ 32 } = 5.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 37° 47'42" } = 13.05 ; ;




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