114 59 61 triangle

Obtuse scalene triangle.

Sides: a = 114   b = 59   c = 61

Area: T = 1067.733030303
Perimeter: p = 234
Semiperimeter: s = 117

Angle ∠ A = α = 143.6055023023° = 143°36'18″ = 2.50663804742 rad
Angle ∠ B = β = 17.88435731154° = 17°53'1″ = 0.31221272329 rad
Angle ∠ C = γ = 18.51114038614° = 18°30'41″ = 0.32330849465 rad

Height: ha = 18.73221105794
Height: hb = 36.19442475602
Height: hc = 35.00875509189

Median: ma = 18.76216630393
Median: mb = 86.53546751308
Median: mc = 85.48883032935

Inradius: r = 9.12659000259
Circumradius: R = 96.06549891731

Vertex coordinates: A[61; 0] B[0; 0] C[108.4921803279; 35.00875509189]
Centroid: CG[56.49772677596; 11.66991836396]
Coordinates of the circumscribed circle: U[30.5; 91.0954632909]
Coordinates of the inscribed circle: I[58; 9.12659000259]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 36.39549769769° = 36°23'42″ = 2.50663804742 rad
∠ B' = β' = 162.1166426885° = 162°6'59″ = 0.31221272329 rad
∠ C' = γ' = 161.4898596139° = 161°29'19″ = 0.32330849465 rad

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How did we calculate this triangle?

a = 114 ; ; b = 59 ; ; c = 61 ; ;

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

p = a+b+c = 114+59+61 = 234 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 234 }{ 2 } = 117 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 117 * (117-114)(117-59)(117-61) } ; ; T = sqrt{ 1140048 } = 1067.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1067.73 }{ 114 } = 18.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1067.73 }{ 59 } = 36.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1067.73 }{ 61 } = 35.01 ; ;

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{ 114**2-59**2-61**2 }{ 2 * 59 * 61 } ) = 143° 36'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 59**2-114**2-61**2 }{ 2 * 114 * 61 } ) = 17° 53'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 61**2-114**2-59**2 }{ 2 * 59 * 114 } ) = 18° 30'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1067.73 }{ 117 } = 9.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 114 }{ 2 * sin 143° 36'18" } = 96.06 ; ;




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