5 19 19 triangle

Acute isosceles triangle.

Sides: a = 5   b = 19   c = 19

Area: T = 47.08770205046
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 15.12216863533° = 15°7'18″ = 0.26439232153 rad
Angle ∠ B = β = 82.43991568233° = 82°26'21″ = 1.43988347191 rad
Angle ∠ C = γ = 82.43991568233° = 82°26'21″ = 1.43988347191 rad

Height: ha = 18.83548082018
Height: hb = 4.95765284742
Height: hc = 4.95765284742

Median: ma = 18.83548082018
Median: mb = 10.13765674664
Median: mc = 10.13765674664

Inradius: r = 2.1990093977
Circumradius: R = 9.58333203113

Vertex coordinates: A[19; 0] B[0; 0] C[0.65878947368; 4.95765284742]
Centroid: CG[6.55326315789; 1.65221761581]
Coordinates of the circumscribed circle: U[9.5; 1.26109631989]
Coordinates of the inscribed circle: I[2.5; 2.1990093977]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.8788313647° = 164°52'42″ = 0.26439232153 rad
∠ B' = β' = 97.56108431767° = 97°33'39″ = 1.43988347191 rad
∠ C' = γ' = 97.56108431767° = 97°33'39″ = 1.43988347191 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 = 19 ; ;

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

p = a+b+c = 5+19+19 = 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 * (21.5-5)(21.5-19)(21.5-19) } ; ; T = sqrt{ 2217.19 } = 47.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.09 }{ 5 } = 18.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.09 }{ 19 } = 4.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.09 }{ 19 } = 4.96 ; ;

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**2-19**2 }{ 2 * 19 * 19 } ) = 15° 7'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-5**2-19**2 }{ 2 * 5 * 19 } ) = 82° 26'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-5**2-19**2 }{ 2 * 19 * 5 } ) = 82° 26'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.09 }{ 21.5 } = 2.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 15° 7'18" } = 9.58 ; ;




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