9 12 19 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 12   c = 19

Area: T = 41.95223539268
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 21.59325161782° = 21°35'33″ = 0.37768605011 rad
Angle ∠ B = β = 29.38546812566° = 29°23'5″ = 0.51328594376 rad
Angle ∠ C = γ = 129.0232802565° = 129°1'22″ = 2.25218727149 rad

Height: ha = 9.32327453171
Height: hb = 6.99220589878
Height: hc = 4.41660372555

Median: ma = 15.24397506541
Median: mb = 13.60114705087
Median: mc = 4.7176990566

Inradius: r = 2.09876176963
Circumradius: R = 12.22881577071

Vertex coordinates: A[19; 0] B[0; 0] C[7.84221052632; 4.41660372555]
Centroid: CG[8.94773684211; 1.47220124185]
Coordinates of the circumscribed circle: U[9.5; -7.69992104082]
Coordinates of the inscribed circle: I[8; 2.09876176963]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.4077483822° = 158°24'27″ = 0.37768605011 rad
∠ B' = β' = 150.6155318743° = 150°36'55″ = 0.51328594376 rad
∠ C' = γ' = 50.97771974348° = 50°58'38″ = 2.25218727149 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 = 9 ; ; b = 12 ; ; c = 19 ; ;

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

p = a+b+c = 9+12+19 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-9)(20-12)(20-19) } ; ; T = sqrt{ 1760 } = 41.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.95 }{ 9 } = 9.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.95 }{ 12 } = 6.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.95 }{ 19 } = 4.42 ; ;

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{ 9**2-12**2-19**2 }{ 2 * 12 * 19 } ) = 21° 35'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-9**2-19**2 }{ 2 * 9 * 19 } ) = 29° 23'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-9**2-12**2 }{ 2 * 12 * 9 } ) = 129° 1'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.95 }{ 20 } = 2.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 21° 35'33" } = 12.23 ; ;




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