2 26 27 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 26   c = 27

Area: T = 22.93333272771
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 3.74662095414° = 3°44'46″ = 0.0655383691 rad
Angle ∠ B = β = 58.1454569176° = 58°8'40″ = 1.01548141743 rad
Angle ∠ C = γ = 118.1099221283° = 118°6'33″ = 2.06113947883 rad

Height: ha = 22.93333272771
Height: hb = 1.76441020982
Height: hc = 1.69987649835

Median: ma = 26.48658452763
Median: mb = 14.05334693226
Median: mc = 12.56598566871

Inradius: r = 0.83439391737
Circumradius: R = 15.30552365999

Vertex coordinates: A[27; 0] B[0; 0] C[1.05655555556; 1.69987649835]
Centroid: CG[9.35218518519; 0.56662549945]
Coordinates of the circumscribed circle: U[13.5; -7.21111210903]
Coordinates of the inscribed circle: I[1.5; 0.83439391737]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.2543790459° = 176°15'14″ = 0.0655383691 rad
∠ B' = β' = 121.8555430824° = 121°51'20″ = 1.01548141743 rad
∠ C' = γ' = 61.89107787174° = 61°53'27″ = 2.06113947883 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 = 2 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 2+26+27 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-2)(27.5-26)(27.5-27) } ; ; T = sqrt{ 525.94 } = 22.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.93 }{ 2 } = 22.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.93 }{ 26 } = 1.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.93 }{ 27 } = 1.7 ; ;

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{ 2**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 3° 44'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-2**2-27**2 }{ 2 * 2 * 27 } ) = 58° 8'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-2**2-26**2 }{ 2 * 26 * 2 } ) = 118° 6'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.93 }{ 27.5 } = 0.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 3° 44'46" } = 15.31 ; ;




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