15 19 28 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 19   c = 28

Area: T = 133.6266344708
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 30.1565906991° = 30°9'21″ = 0.52663198659 rad
Angle ∠ B = β = 39.51876527972° = 39°31'4″ = 0.6989713154 rad
Angle ∠ C = γ = 110.3266440212° = 110°19'35″ = 1.92655596337 rad

Height: ha = 17.81768459611
Height: hb = 14.06659310219
Height: hc = 9.54547389077

Median: ma = 22.7211135535
Median: mb = 20.3533132437
Median: mc = 9.84988578018

Inradius: r = 4.31105272486
Circumradius: R = 14.9329690731

Vertex coordinates: A[28; 0] B[0; 0] C[11.57114285714; 9.54547389077]
Centroid: CG[13.19904761905; 3.18215796359]
Coordinates of the circumscribed circle: U[14; -5.1866103096]
Coordinates of the inscribed circle: I[12; 4.31105272486]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.8444093009° = 149°50'39″ = 0.52663198659 rad
∠ B' = β' = 140.4822347203° = 140°28'56″ = 0.6989713154 rad
∠ C' = γ' = 69.67435597882° = 69°40'25″ = 1.92655596337 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 = 15 ; ; b = 19 ; ; c = 28 ; ;

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

p = a+b+c = 15+19+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 * (31-15)(31-19)(31-28) } ; ; T = sqrt{ 17856 } = 133.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 133.63 }{ 15 } = 17.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 133.63 }{ 19 } = 14.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 133.63 }{ 28 } = 9.54 ; ;

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{ 15**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 30° 9'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 39° 31'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-19**2 }{ 2 * 19 * 15 } ) = 110° 19'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 133.63 }{ 31 } = 4.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 30° 9'21" } = 14.93 ; ;




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