14 20 26 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 20   c = 26

Area: T = 138.5644064605
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 32.2044227504° = 32°12'15″ = 0.5622069803 rad
Angle ∠ B = β = 49.58325617943° = 49°34'57″ = 0.86553789549 rad
Angle ∠ C = γ = 98.21332107017° = 98°12'48″ = 1.71441438957 rad

Height: ha = 19.79548663722
Height: hb = 13.85664064606
Height: hc = 10.65987742004

Median: ma = 22.11333443875
Median: mb = 18.33303027798
Median: mc = 11.35878166916

Inradius: r = 4.61988021535
Circumradius: R = 13.13547186241

Vertex coordinates: A[26; 0] B[0; 0] C[9.07769230769; 10.65987742004]
Centroid: CG[11.69223076923; 3.55329247335]
Coordinates of the circumscribed circle: U[13; -1.87663883749]
Coordinates of the inscribed circle: I[10; 4.61988021535]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.7965772496° = 147°47'45″ = 0.5622069803 rad
∠ B' = β' = 130.4177438206° = 130°25'3″ = 0.86553789549 rad
∠ C' = γ' = 81.78767892983° = 81°47'12″ = 1.71441438957 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 = 20 ; ; c = 26 ; ;

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

p = a+b+c = 14+20+26 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-14)(30-20)(30-26) } ; ; T = sqrt{ 19200 } = 138.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 138.56 }{ 14 } = 19.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 138.56 }{ 20 } = 13.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 138.56 }{ 26 } = 10.66 ; ;

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**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 32° 12'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 49° 34'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-20**2 }{ 2 * 20 * 14 } ) = 98° 12'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 138.56 }{ 30 } = 4.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 32° 12'15" } = 13.13 ; ;




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