4 16 19 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 16   c = 19

Area: T = 22.99986412642
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 8.7032668043° = 8°42'10″ = 0.15218902111 rad
Angle ∠ B = β = 37.24552073039° = 37°14'43″ = 0.6550051498 rad
Angle ∠ C = γ = 134.0522124653° = 134°3'8″ = 2.34396509445 rad

Height: ha = 11.49993206321
Height: hb = 2.8754830158
Height: hc = 2.42109096068

Median: ma = 17.45499283666
Median: mb = 11.15879568022
Median: mc = 6.76438746292

Inradius: r = 1.17994175007
Circumradius: R = 13.21881721741

Vertex coordinates: A[19; 0] B[0; 0] C[3.18442105263; 2.42109096068]
Centroid: CG[7.39547368421; 0.80769698689]
Coordinates of the circumscribed circle: U[9.5; -9.19107603398]
Coordinates of the inscribed circle: I[3.5; 1.17994175007]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.2977331957° = 171°17'50″ = 0.15218902111 rad
∠ B' = β' = 142.7554792696° = 142°45'17″ = 0.6550051498 rad
∠ C' = γ' = 45.94878753469° = 45°56'52″ = 2.34396509445 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 = 4 ; ; b = 16 ; ; c = 19 ; ;

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

p = a+b+c = 4+16+19 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-4)(19.5-16)(19.5-19) } ; ; T = sqrt{ 528.94 } = 23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23 }{ 4 } = 11.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23 }{ 16 } = 2.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23 }{ 19 } = 2.42 ; ;

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{ 4**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 8° 42'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-4**2-19**2 }{ 2 * 4 * 19 } ) = 37° 14'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-4**2-16**2 }{ 2 * 16 * 4 } ) = 134° 3'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23 }{ 19.5 } = 1.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 8° 42'10" } = 13.22 ; ;




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