14 19 25 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 19   c = 25

Area: T = 131.9099059583
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 33.73987226487° = 33°44'19″ = 0.58988517956 rad
Angle ∠ B = β = 48.91876668595° = 48°55'4″ = 0.85437743491 rad
Angle ∠ C = γ = 97.34436104917° = 97°20'37″ = 1.69989665089 rad

Height: ha = 18.8444151369
Height: hb = 13.88551641666
Height: hc = 10.55327247666

Median: ma = 21.07113075057
Median: mb = 17.89655301682
Median: mc = 11.05766721937

Inradius: r = 4.54985882615
Circumradius: R = 12.60333799745

Vertex coordinates: A[25; 0] B[0; 0] C[9.2; 10.55327247666]
Centroid: CG[11.4; 3.51875749222]
Coordinates of the circumscribed circle: U[12.5; -1.61109583426]
Coordinates of the inscribed circle: I[10; 4.54985882615]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.2611277351° = 146°15'41″ = 0.58988517956 rad
∠ B' = β' = 131.082233314° = 131°4'56″ = 0.85437743491 rad
∠ C' = γ' = 82.65663895083° = 82°39'23″ = 1.69989665089 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 = 14 ; ; b = 19 ; ; c = 25 ; ;

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

p = a+b+c = 14+19+25 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-14)(29-19)(29-25) } ; ; T = sqrt{ 17400 } = 131.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.91 }{ 14 } = 18.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.91 }{ 19 } = 13.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.91 }{ 25 } = 10.55 ; ;

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{ 14**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 33° 44'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 48° 55'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-19**2 }{ 2 * 19 * 14 } ) = 97° 20'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.91 }{ 29 } = 4.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 33° 44'19" } = 12.6 ; ;




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