100 60 159 triangle

Obtuse scalene triangle.

Sides: a = 100   b = 60   c = 159

Area: T = 687.1244397398
Perimeter: p = 319
Semiperimeter: s = 159.5

Angle ∠ A = α = 8.28223422543° = 8°16'56″ = 0.14545541421 rad
Angle ∠ B = β = 4.95883031558° = 4°57'30″ = 0.08765387154 rad
Angle ∠ C = γ = 166.759935459° = 166°45'34″ = 2.91104997961 rad

Height: ha = 13.7422487948
Height: hb = 22.90441465799
Height: hc = 8.64330741811

Median: ma = 109.2732594918
Median: mb = 129.3855084148
Median: mc = 21.90331961138

Inradius: r = 4.30879899523
Circumradius: R = 347.0998721721

Vertex coordinates: A[159; 0] B[0; 0] C[99.62657861635; 8.64330741811]
Centroid: CG[86.20985953878; 2.8811024727]
Coordinates of the circumscribed circle: U[79.5; -337.8721680701]
Coordinates of the inscribed circle: I[99.5; 4.30879899523]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.7187657746° = 171°43'4″ = 0.14545541421 rad
∠ B' = β' = 175.0421696844° = 175°2'30″ = 0.08765387154 rad
∠ C' = γ' = 13.24106454101° = 13°14'26″ = 2.91104997961 rad

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How did we calculate this triangle?

a = 100 ; ; b = 60 ; ; c = 159 ; ;

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

p = a+b+c = 100+60+159 = 319 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 319 }{ 2 } = 159.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 159.5 * (159.5-100)(159.5-60)(159.5-159) } ; ; T = sqrt{ 472139.94 } = 687.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 687.12 }{ 100 } = 13.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 687.12 }{ 60 } = 22.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 687.12 }{ 159 } = 8.64 ; ;

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{ 100**2-60**2-159**2 }{ 2 * 60 * 159 } ) = 8° 16'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60**2-100**2-159**2 }{ 2 * 100 * 159 } ) = 4° 57'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 159**2-100**2-60**2 }{ 2 * 60 * 100 } ) = 166° 45'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 687.12 }{ 159.5 } = 4.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 8° 16'56" } = 347.1 ; ;




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