19 22 30 triangle

Obtuse scalene triangle.

Sides: a = 19   b = 22   c = 30

Area: T = 208.5477206886
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 39.1954967426° = 39°11'42″ = 0.68440812318 rad
Angle ∠ B = β = 47.0332848889° = 47°1'58″ = 0.82108780697 rad
Angle ∠ C = γ = 93.77221836851° = 93°46'20″ = 1.63766333521 rad

Height: ha = 21.9522337567
Height: hb = 18.95988369896
Height: hc = 13.90331471257

Median: ma = 24.53105931441
Median: mb = 22.57221066806
Median: mc = 14.05334693226

Inradius: r = 5.87545692081
Circumradius: R = 15.03325676705

Vertex coordinates: A[30; 0] B[0; 0] C[12.95; 13.90331471257]
Centroid: CG[14.31766666667; 4.63443823752]
Coordinates of the circumscribed circle: U[15; -0.98989847152]
Coordinates of the inscribed circle: I[13.5; 5.87545692081]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.8055032574° = 140°48'18″ = 0.68440812318 rad
∠ B' = β' = 132.9677151111° = 132°58'2″ = 0.82108780697 rad
∠ C' = γ' = 86.22878163149° = 86°13'40″ = 1.63766333521 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 = 22 ; ; c = 30 ; ;

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

p = a+b+c = 19+22+30 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-19)(35.5-22)(35.5-30) } ; ; T = sqrt{ 43491.94 } = 208.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 208.55 }{ 19 } = 21.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 208.55 }{ 22 } = 18.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 208.55 }{ 30 } = 13.9 ; ;

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**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 39° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 47° 1'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-19**2-22**2 }{ 2 * 22 * 19 } ) = 93° 46'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 208.55 }{ 35.5 } = 5.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 39° 11'42" } = 15.03 ; ;




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