11 16 20 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 16   c = 20

Area: T = 87.81219439484
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 33.28664163383° = 33°17'11″ = 0.58109575613 rad
Angle ∠ B = β = 52.9677156255° = 52°58'2″ = 0.92444512721 rad
Angle ∠ C = γ = 93.74664274067° = 93°44'47″ = 1.63661838202 rad

Height: ha = 15.96658079906
Height: hb = 10.97664929936
Height: hc = 8.78111943948

Median: ma = 17.25554339267
Median: mb = 14.01878457689
Median: mc = 9.40774438611

Inradius: r = 3.73766784659
Circumradius: R = 10.02114157714

Vertex coordinates: A[20; 0] B[0; 0] C[6.625; 8.78111943948]
Centroid: CG[8.875; 2.92770647983]
Coordinates of the circumscribed circle: U[10; -0.65548084169]
Coordinates of the inscribed circle: I[7.5; 3.73766784659]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7143583662° = 146°42'49″ = 0.58109575613 rad
∠ B' = β' = 127.0332843745° = 127°1'58″ = 0.92444512721 rad
∠ C' = γ' = 86.25435725933° = 86°15'13″ = 1.63661838202 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 = 16 ; ; c = 20 ; ;

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

p = a+b+c = 11+16+20 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-11)(23.5-16)(23.5-20) } ; ; T = sqrt{ 7710.94 } = 87.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 87.81 }{ 11 } = 15.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 87.81 }{ 16 } = 10.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 87.81 }{ 20 } = 8.78 ; ;

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**2-16**2-20**2 }{ 2 * 16 * 20 } ) = 33° 17'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-11**2-20**2 }{ 2 * 11 * 20 } ) = 52° 58'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-11**2-16**2 }{ 2 * 16 * 11 } ) = 93° 44'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 87.81 }{ 23.5 } = 3.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 33° 17'11" } = 10.02 ; ;




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