14 19 26 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 19   c = 26

Area: T = 129.6330002314
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 31.65659800068° = 31°39'22″ = 0.55325010791 rad
Angle ∠ B = β = 45.41985029197° = 45°25'7″ = 0.79327024173 rad
Angle ∠ C = γ = 102.9265517073° = 102°55'32″ = 1.79663891572 rad

Height: ha = 18.51985717592
Height: hb = 13.64552634015
Height: hc = 9.97215386396

Median: ma = 21.668794868
Median: mb = 18.59443539818
Median: mc = 10.46442247682

Inradius: r = 4.39442373666
Circumradius: R = 13.33879616534

Vertex coordinates: A[26; 0] B[0; 0] C[9.82769230769; 9.97215386396]
Centroid: CG[11.94223076923; 3.32438462132]
Coordinates of the circumscribed circle: U[13; -2.98334914225]
Coordinates of the inscribed circle: I[10.5; 4.39442373666]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.3444019993° = 148°20'38″ = 0.55325010791 rad
∠ B' = β' = 134.581149708° = 134°34'53″ = 0.79327024173 rad
∠ C' = γ' = 77.07444829265° = 77°4'28″ = 1.79663891572 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 = 26 ; ;

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

p = a+b+c = 14+19+26 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-14)(29.5-19)(29.5-26) } ; ; T = sqrt{ 16803.94 } = 129.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 129.63 }{ 14 } = 18.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 129.63 }{ 19 } = 13.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 129.63 }{ 26 } = 9.97 ; ;

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**2-26**2 }{ 2 * 19 * 26 } ) = 31° 39'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 45° 25'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-19**2 }{ 2 * 19 * 14 } ) = 102° 55'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 129.63 }{ 29.5 } = 4.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 31° 39'22" } = 13.34 ; ;




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