240 127 281 triangle

Obtuse scalene triangle.

Sides: a = 240   b = 127   c = 281

Area: T = 15183.76655409
Perimeter: p = 648
Semiperimeter: s = 324

Angle ∠ A = α = 58.31441645186° = 58°18'51″ = 1.01877741714 rad
Angle ∠ B = β = 26.76222663382° = 26°45'44″ = 0.46770896629 rad
Angle ∠ C = γ = 94.92435691432° = 94°55'25″ = 1.65767288193 rad

Height: ha = 126.5311379507
Height: hb = 239.1144417966
Height: hc = 108.0769505629

Median: ma = 182.0587683167
Median: mb = 253.4722385084
Median: mc = 130.8659657649

Inradius: r = 46.86334738916
Circumradius: R = 141.0220354551

Vertex coordinates: A[281; 0] B[0; 0] C[214.2921814947; 108.0769505629]
Centroid: CG[165.0977271649; 36.0233168543]
Coordinates of the circumscribed circle: U[140.5; -12.10333217686]
Coordinates of the inscribed circle: I[197; 46.86334738916]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.6865835481° = 121°41'9″ = 1.01877741714 rad
∠ B' = β' = 153.2387733662° = 153°14'16″ = 0.46770896629 rad
∠ C' = γ' = 85.07664308568° = 85°4'35″ = 1.65767288193 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 = 240 ; ; b = 127 ; ; c = 281 ; ;

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

p = a+b+c = 240+127+281 = 648 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 648 }{ 2 } = 324 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 324 * (324-240)(324-127)(324-281) } ; ; T = sqrt{ 230546736 } = 15183.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15183.77 }{ 240 } = 126.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15183.77 }{ 127 } = 239.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15183.77 }{ 281 } = 108.07 ; ;

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{ 240**2-127**2-281**2 }{ 2 * 127 * 281 } ) = 58° 18'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 127**2-240**2-281**2 }{ 2 * 240 * 281 } ) = 26° 45'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 281**2-240**2-127**2 }{ 2 * 127 * 240 } ) = 94° 55'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15183.77 }{ 324 } = 46.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 240 }{ 2 * sin 58° 18'51" } = 141.02 ; ;




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