11 23 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 23   c = 28

Area: T = 121.9843605456
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 22.26112954012° = 22°15'41″ = 0.38985329005 rad
Angle ∠ B = β = 52.38223203336° = 52°22'56″ = 0.91442439597 rad
Angle ∠ C = γ = 105.3566384265° = 105°21'23″ = 1.83988157934 rad

Height: ha = 22.17988373556
Height: hb = 10.60772700396
Height: hc = 8.71331146754

Median: ma = 25.02549875125
Median: mb = 17.89655301682
Median: mc = 11.35878166916

Inradius: r = 3.93549550147
Circumradius: R = 14.51883444397

Vertex coordinates: A[28; 0] B[0; 0] C[6.71442857143; 8.71331146754]
Centroid: CG[11.57114285714; 2.90443715585]
Coordinates of the circumscribed circle: U[14; -3.84547789623]
Coordinates of the inscribed circle: I[8; 3.93549550147]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.7398704599° = 157°44'19″ = 0.38985329005 rad
∠ B' = β' = 127.6187679666° = 127°37'4″ = 0.91442439597 rad
∠ C' = γ' = 74.64436157347° = 74°38'37″ = 1.83988157934 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 = 23 ; ; c = 28 ; ;

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

p = a+b+c = 11+23+28 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-11)(31-23)(31-28) } ; ; T = sqrt{ 14880 } = 121.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 121.98 }{ 11 } = 22.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 121.98 }{ 23 } = 10.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 121.98 }{ 28 } = 8.71 ; ;

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**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 22° 15'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 52° 22'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-23**2 }{ 2 * 23 * 11 } ) = 105° 21'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 121.98 }{ 31 } = 3.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 22° 15'41" } = 14.52 ; ;




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