11 21 26 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 21   c = 26

Area: T = 111.9298548637
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 24.20545008373° = 24°12'16″ = 0.42224482334 rad
Angle ∠ B = β = 51.51100302971° = 51°30'36″ = 0.89990196265 rad
Angle ∠ C = γ = 104.2855468866° = 104°17'8″ = 1.82201247937 rad

Height: ha = 20.35106452067
Height: hb = 10.6659861775
Height: hc = 8.61098883567

Median: ma = 22.98436898691
Median: mb = 16.97879268463
Median: mc = 10.58330052443

Inradius: r = 3.86596051254
Circumradius: R = 13.41548080922

Vertex coordinates: A[26; 0] B[0; 0] C[6.84661538462; 8.61098883567]
Centroid: CG[10.94987179487; 2.87699627856]
Coordinates of the circumscribed circle: U[13; -3.31101474513]
Coordinates of the inscribed circle: I[8; 3.86596051254]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.7955499163° = 155°47'44″ = 0.42224482334 rad
∠ B' = β' = 128.4989969703° = 128°29'24″ = 0.89990196265 rad
∠ C' = γ' = 75.71545311344° = 75°42'52″ = 1.82201247937 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 = 11 ; ; b = 21 ; ; c = 26 ; ;

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

p = a+b+c = 11+21+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 * (29-11)(29-21)(29-26) } ; ; T = sqrt{ 12528 } = 111.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 111.93 }{ 11 } = 20.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 111.93 }{ 21 } = 10.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 111.93 }{ 26 } = 8.61 ; ;

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{ 11**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 24° 12'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-11**2-26**2 }{ 2 * 11 * 26 } ) = 51° 30'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-11**2-21**2 }{ 2 * 21 * 11 } ) = 104° 17'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 111.93 }{ 29 } = 3.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 24° 12'16" } = 13.41 ; ;




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