5 19 20 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 19   c = 20

Area: T = 47.37108771293
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 14.43773009655° = 14°26'14″ = 0.25219784369 rad
Angle ∠ B = β = 71.33770751151° = 71°20'13″ = 1.24550668395 rad
Angle ∠ C = γ = 94.22656239195° = 94°13'32″ = 1.64545473771 rad

Height: ha = 18.94883508517
Height: hb = 4.98664081189
Height: hc = 4.73770877129

Median: ma = 19.34655421222
Median: mb = 11.05766721937
Median: mc = 9.6443650761

Inradius: r = 2.15332216877
Circumradius: R = 10.02772578594

Vertex coordinates: A[20; 0] B[0; 0] C[1.6; 4.73770877129]
Centroid: CG[7.2; 1.57990292376]
Coordinates of the circumscribed circle: U[10; -0.73988505791]
Coordinates of the inscribed circle: I[3; 2.15332216877]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.5632699035° = 165°33'46″ = 0.25219784369 rad
∠ B' = β' = 108.6632924885° = 108°39'47″ = 1.24550668395 rad
∠ C' = γ' = 85.77443760805° = 85°46'28″ = 1.64545473771 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 = 5 ; ; b = 19 ; ; c = 20 ; ;

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

p = a+b+c = 5+19+20 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-5)(22-19)(22-20) } ; ; T = sqrt{ 2244 } = 47.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.37 }{ 5 } = 18.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.37 }{ 19 } = 4.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.37 }{ 20 } = 4.74 ; ;

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{ 5**2-19**2-20**2 }{ 2 * 19 * 20 } ) = 14° 26'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-5**2-20**2 }{ 2 * 5 * 20 } ) = 71° 20'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-5**2-19**2 }{ 2 * 19 * 5 } ) = 94° 13'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.37 }{ 22 } = 2.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 14° 26'14" } = 10.03 ; ;




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