19 20 30 triangle

Obtuse scalene triangle.

Sides: a = 19   b = 20   c = 30

Area: T = 186.7955175259
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 38.51099535886° = 38°30'36″ = 0.67221254849 rad
Angle ∠ B = β = 40.95216307599° = 40°57'6″ = 0.71547407908 rad
Angle ∠ C = γ = 100.5388415652° = 100°32'18″ = 1.75547263779 rad

Height: ha = 19.66326500273
Height: hb = 18.68795175259
Height: hc = 12.45330116839

Median: ma = 23.65990363286
Median: mb = 23.03325856126
Median: mc = 12.47699639133

Inradius: r = 5.41443529061
Circumradius: R = 15.25773533875

Vertex coordinates: A[30; 0] B[0; 0] C[14.35; 12.45330116839]
Centroid: CG[14.78333333333; 4.15110038946]
Coordinates of the circumscribed circle: U[15; -2.79904896327]
Coordinates of the inscribed circle: I[14.5; 5.41443529061]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.4990046411° = 141°29'24″ = 0.67221254849 rad
∠ B' = β' = 139.048836924° = 139°2'54″ = 0.71547407908 rad
∠ C' = γ' = 79.46215843485° = 79°27'42″ = 1.75547263779 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 = 19 ; ; b = 20 ; ; c = 30 ; ;

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

p = a+b+c = 19+20+30 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-19)(34.5-20)(34.5-30) } ; ; T = sqrt{ 34892.44 } = 186.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 186.8 }{ 19 } = 19.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 186.8 }{ 20 } = 18.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 186.8 }{ 30 } = 12.45 ; ;

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{ 19**2-20**2-30**2 }{ 2 * 20 * 30 } ) = 38° 30'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 40° 57'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-19**2-20**2 }{ 2 * 20 * 19 } ) = 100° 32'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 186.8 }{ 34.5 } = 5.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 38° 30'36" } = 15.26 ; ;




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