10 19 28 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 19   c = 28

Area: T = 50.04443553261
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 10.84440625637° = 10°50'39″ = 0.1899264596 rad
Angle ∠ B = β = 20.94442680534° = 20°56'39″ = 0.3665546437 rad
Angle ∠ C = γ = 148.2121669383° = 148°12'42″ = 2.58767816206 rad

Height: ha = 10.00988710652
Height: hb = 5.26878268764
Height: hc = 3.5754596809

Median: ma = 23.39987179136
Median: mb = 18.75549993335
Median: mc = 5.87436700622

Inradius: r = 1.75659422921
Circumradius: R = 26.57664238811

Vertex coordinates: A[28; 0] B[0; 0] C[9.33992857143; 3.5754596809]
Centroid: CG[12.44664285714; 1.19215322697]
Coordinates of the circumscribed circle: U[14; -22.59899602989]
Coordinates of the inscribed circle: I[9.5; 1.75659422921]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.1565937436° = 169°9'21″ = 0.1899264596 rad
∠ B' = β' = 159.0565731947° = 159°3'21″ = 0.3665546437 rad
∠ C' = γ' = 31.78883306171° = 31°47'18″ = 2.58767816206 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 = 10 ; ; b = 19 ; ; c = 28 ; ;

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

p = a+b+c = 10+19+28 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-10)(28.5-19)(28.5-28) } ; ; T = sqrt{ 2504.44 } = 50.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.04 }{ 10 } = 10.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.04 }{ 19 } = 5.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.04 }{ 28 } = 3.57 ; ;

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{ 10**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 10° 50'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-10**2-28**2 }{ 2 * 10 * 28 } ) = 20° 56'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-10**2-19**2 }{ 2 * 19 * 10 } ) = 148° 12'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.04 }{ 28.5 } = 1.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 10° 50'39" } = 26.58 ; ;




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