6 26 27 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 26   c = 27

Area: T = 77.88441286784
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 12.82201897405° = 12°49'13″ = 0.22437545217 rad
Angle ∠ B = β = 74.05663780336° = 74°3'23″ = 1.29325276288 rad
Angle ∠ C = γ = 93.12334322259° = 93°7'24″ = 1.62553105031 rad

Height: ha = 25.96113762261
Height: hb = 5.99110868214
Height: hc = 5.76991947169

Median: ma = 26.33443881645
Median: mb = 14.61216391962
Median: mc = 13.18114263265

Inradius: r = 2.64401399552
Circumradius: R = 13.52200844879

Vertex coordinates: A[27; 0] B[0; 0] C[1.64881481481; 5.76991947169]
Centroid: CG[9.5499382716; 1.92330649056]
Coordinates of the circumscribed circle: U[13.5; -0.73766712702]
Coordinates of the inscribed circle: I[3.5; 2.64401399552]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.187981026° = 167°10'47″ = 0.22437545217 rad
∠ B' = β' = 105.9443621966° = 105°56'37″ = 1.29325276288 rad
∠ C' = γ' = 86.87765677741° = 86°52'36″ = 1.62553105031 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 = 6 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 6+26+27 = 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 * (29.5-6)(29.5-26)(29.5-27) } ; ; T = sqrt{ 6065.94 } = 77.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 77.88 }{ 6 } = 25.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 77.88 }{ 26 } = 5.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 77.88 }{ 27 } = 5.77 ; ;

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{ 6**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 12° 49'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-6**2-27**2 }{ 2 * 6 * 27 } ) = 74° 3'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-6**2-26**2 }{ 2 * 26 * 6 } ) = 93° 7'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 77.88 }{ 29.5 } = 2.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 12° 49'13" } = 13.52 ; ;




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