16 19 28 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 19   c = 28

Area: T = 146.1543814524
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 33.32993183747° = 33°19'46″ = 0.58217063431 rad
Angle ∠ B = β = 40.72882696126° = 40°43'42″ = 0.71108424034 rad
Angle ∠ C = γ = 105.9422412013° = 105°56'33″ = 1.84990439071 rad

Height: ha = 18.26992268155
Height: hb = 15.38546120552
Height: hc = 10.44395581803

Median: ma = 22.55499445676
Median: mb = 20.73304124416
Median: mc = 10.60766017178

Inradius: r = 4.64398036357
Circumradius: R = 14.5660003151

Vertex coordinates: A[28; 0] B[0; 0] C[12.125; 10.44395581803]
Centroid: CG[13.375; 3.48798527268]
Coordinates of the circumscribed circle: U[14; -3.99992113918]
Coordinates of the inscribed circle: I[12.5; 4.64398036357]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.6710681625° = 146°40'14″ = 0.58217063431 rad
∠ B' = β' = 139.2721730387° = 139°16'18″ = 0.71108424034 rad
∠ C' = γ' = 74.05875879874° = 74°3'27″ = 1.84990439071 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 = 16 ; ; b = 19 ; ; c = 28 ; ;

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

p = a+b+c = 16+19+28 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-16)(31.5-19)(31.5-28) } ; ; T = sqrt{ 21360.94 } = 146.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 146.15 }{ 16 } = 18.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 146.15 }{ 19 } = 15.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 146.15 }{ 28 } = 10.44 ; ;

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{ 16**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 33° 19'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 40° 43'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-19**2 }{ 2 * 19 * 16 } ) = 105° 56'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 146.15 }{ 31.5 } = 4.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 33° 19'46" } = 14.56 ; ;




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