4 26 27 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 26   c = 27

Area: T = 51.17106703102
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 8.38327617612° = 8°22'58″ = 0.14663067931 rad
Angle ∠ B = β = 71.37106694253° = 71°22'14″ = 1.24656531708 rad
Angle ∠ C = γ = 100.2476568814° = 100°14'48″ = 1.75496326896 rad

Height: ha = 25.58553351551
Height: hb = 3.93662054085
Height: hc = 3.7990420023

Median: ma = 26.42991505728
Median: mb = 14.26553426177
Median: mc = 12.79664838921

Inradius: r = 1.79554621161
Circumradius: R = 13.71987962507

Vertex coordinates: A[27; 0] B[0; 0] C[1.27877777778; 3.7990420023]
Centroid: CG[9.42659259259; 1.2633473341]
Coordinates of the circumscribed circle: U[13.5; -2.44403627946]
Coordinates of the inscribed circle: I[2.5; 1.79554621161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.6177238239° = 171°37'2″ = 0.14663067931 rad
∠ B' = β' = 108.6299330575° = 108°37'46″ = 1.24656531708 rad
∠ C' = γ' = 79.75334311865° = 79°45'12″ = 1.75496326896 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 = 4 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 4+26+27 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-4)(28.5-26)(28.5-27) } ; ; T = sqrt{ 2618.44 } = 51.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.17 }{ 4 } = 25.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.17 }{ 26 } = 3.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.17 }{ 27 } = 3.79 ; ;

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{ 4**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 8° 22'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-4**2-27**2 }{ 2 * 4 * 27 } ) = 71° 22'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-4**2-26**2 }{ 2 * 26 * 4 } ) = 100° 14'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.17 }{ 28.5 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 8° 22'58" } = 13.72 ; ;




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