4 19 20 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 19   c = 20

Area: T = 37.56224480033
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 11.40223236093° = 11°24'8″ = 0.19990080894 rad
Angle ∠ B = β = 69.89444902121° = 69°53'40″ = 1.22198889832 rad
Angle ∠ C = γ = 98.70331861786° = 98°42'11″ = 1.7232695581 rad

Height: ha = 18.78112240016
Height: hb = 3.95439418951
Height: hc = 3.75662448003

Median: ma = 19.40436079119
Median: mb = 10.85112672071
Median: mc = 9.40774438611

Inradius: r = 1.74770906048
Circumradius: R = 10.11664865497

Vertex coordinates: A[20; 0] B[0; 0] C[1.375; 3.75662448003]
Centroid: CG[7.125; 1.25220816001]
Coordinates of the circumscribed circle: U[10; -1.5310784149]
Coordinates of the inscribed circle: I[2.5; 1.74770906048]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5987676391° = 168°35'52″ = 0.19990080894 rad
∠ B' = β' = 110.1065509788° = 110°6'20″ = 1.22198889832 rad
∠ C' = γ' = 81.29768138214° = 81°17'49″ = 1.7232695581 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 = 19 ; ; c = 20 ; ;

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

p = a+b+c = 4+19+20 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-4)(21.5-19)(21.5-20) } ; ; T = sqrt{ 1410.94 } = 37.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.56 }{ 4 } = 18.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.56 }{ 19 } = 3.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.56 }{ 20 } = 3.76 ; ;

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**2-19**2-20**2 }{ 2 * 19 * 20 } ) = 11° 24'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-4**2-20**2 }{ 2 * 4 * 20 } ) = 69° 53'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-4**2-19**2 }{ 2 * 19 * 4 } ) = 98° 42'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.56 }{ 21.5 } = 1.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 11° 24'8" } = 10.12 ; ;




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