11 19 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 19   c = 28

Area: T = 72.25495674728
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 15.76603863421° = 15°45'37″ = 0.27550706331 rad
Angle ∠ B = β = 27.97993322757° = 27°58'46″ = 0.48883314707 rad
Angle ∠ C = γ = 136.2660281382° = 136°15'37″ = 2.37881905498 rad

Height: ha = 13.1366284995
Height: hb = 7.60552176287
Height: hc = 5.16106833909

Median: ma = 23.28662620444
Median: mb = 19.03328663107
Median: mc = 6.70882039325

Inradius: r = 2.49113643956
Circumradius: R = 20.2499256171

Vertex coordinates: A[28; 0] B[0; 0] C[9.71442857143; 5.16106833909]
Centroid: CG[12.57114285714; 1.7220227797]
Coordinates of the circumscribed circle: U[14; -14.63298453676]
Coordinates of the inscribed circle: I[10; 2.49113643956]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.2439613658° = 164°14'23″ = 0.27550706331 rad
∠ B' = β' = 152.0210667724° = 152°1'14″ = 0.48883314707 rad
∠ C' = γ' = 43.74397186178° = 43°44'23″ = 2.37881905498 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 = 19 ; ; c = 28 ; ;

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

p = a+b+c = 11+19+28 = 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)(29-19)(29-28) } ; ; T = sqrt{ 5220 } = 72.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72.25 }{ 11 } = 13.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72.25 }{ 19 } = 7.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72.25 }{ 28 } = 5.16 ; ;

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**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 15° 45'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 27° 58'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-19**2 }{ 2 * 19 * 11 } ) = 136° 15'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72.25 }{ 29 } = 2.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 15° 45'37" } = 20.25 ; ;




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