6960 5535 8895 triangle

Obtuse scalene triangle.

Sides: a = 6960   b = 5535   c = 8895

Area: T = 19261796.97222
Perimeter: p = 21390
Semiperimeter: s = 10695

Angle ∠ A = α = 51.48765437762° = 51°29'12″ = 0.89986097094 rad
Angle ∠ B = β = 38.481133075° = 38°28'53″ = 0.67216259221 rad
Angle ∠ C = γ = 90.03221254738° = 90°1'56″ = 1.57113570221 rad

Height: ha = 5534.999912996
Height: hb = 6959.999890596
Height: hc = 4330.927680658

Median: ma = 6539.742196739
Median: mb = 7491.47989094
Median: mc = 4445.071100618

Inradius: r = 1801.010953457
Circumradius: R = 4447.50106991

Vertex coordinates: A[8895; 0] B[0; 0] C[5448.364424958; 4330.927680658]
Centroid: CG[4781.121141653; 1443.642226886]
Coordinates of the circumscribed circle: U[4447.5; -2.49436925703]
Coordinates of the inscribed circle: I[5160; 1801.010953457]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.5133456224° = 128°30'48″ = 0.89986097094 rad
∠ B' = β' = 141.519866925° = 141°31'7″ = 0.67216259221 rad
∠ C' = γ' = 89.96878745262° = 89°58'4″ = 1.57113570221 rad

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How did we calculate this triangle?

a = 6960 ; ; b = 5535 ; ; c = 8895 ; ;

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

p = a+b+c = 6960+5535+8895 = 21390 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21390 }{ 2 } = 10695 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10695 * (10695-6960)(10695-5535)(10695-8895) } ; ; T = sqrt{ 3.71 * 10**{ 14 } } = 19261796.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19261796.97 }{ 6960 } = 5535 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19261796.97 }{ 5535 } = 6960 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19261796.97 }{ 8895 } = 4330.93 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 5535**2+8895**2-6960**2 }{ 2 * 5535 * 8895 } ) = 51° 29'12" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6960**2+8895**2-5535**2 }{ 2 * 6960 * 8895 } ) = 38° 28'53" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 6960**2+5535**2-8895**2 }{ 2 * 6960 * 5535 } ) = 90° 1'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19261796.97 }{ 10695 } = 1801.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6960 }{ 2 * sin 51° 29'12" } = 4447.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5535**2+2 * 8895**2 - 6960**2 } }{ 2 } = 6539.742 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8895**2+2 * 6960**2 - 5535**2 } }{ 2 } = 7491.479 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5535**2+2 * 6960**2 - 8895**2 } }{ 2 } = 4445.071 ; ;
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