140 247 360 triangle

Obtuse scalene triangle.

Sides: a = 140   b = 247   c = 360

Area: T = 12203.96332881
Perimeter: p = 747
Semiperimeter: s = 373.5

Angle ∠ A = α = 15.93218086017° = 15°55'55″ = 0.27880625159 rad
Angle ∠ B = β = 28.96655895447° = 28°57'56″ = 0.50655449073 rad
Angle ∠ C = γ = 135.1032601854° = 135°6'9″ = 2.35879852304 rad

Height: ha = 174.3422332687
Height: hb = 98.81875165029
Height: hc = 67.8799796045

Median: ma = 300.6733410863
Median: mb = 243.6143936383
Median: mc = 88.9077255047

Inradius: r = 32.67546005036
Circumradius: R = 255.0165516396

Vertex coordinates: A[360; 0] B[0; 0] C[122.48875; 67.8799796045]
Centroid: CG[160.8299166667; 22.6599932015]
Coordinates of the circumscribed circle: U[180; -180.6465823652]
Coordinates of the inscribed circle: I[126.5; 32.67546005036]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.0688191398° = 164°4'5″ = 0.27880625159 rad
∠ B' = β' = 151.0344410455° = 151°2'4″ = 0.50655449073 rad
∠ C' = γ' = 44.89773981463° = 44°53'51″ = 2.35879852304 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 = 140 ; ; b = 247 ; ; c = 360 ; ;

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

p = a+b+c = 140+247+360 = 747 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 747 }{ 2 } = 373.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 373.5 * (373.5-140)(373.5-247)(373.5-360) } ; ; T = sqrt{ 148936719.94 } = 12203.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12203.96 }{ 140 } = 174.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12203.96 }{ 247 } = 98.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12203.96 }{ 360 } = 67.8 ; ;

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{ 140**2-247**2-360**2 }{ 2 * 247 * 360 } ) = 15° 55'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 247**2-140**2-360**2 }{ 2 * 140 * 360 } ) = 28° 57'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 360**2-140**2-247**2 }{ 2 * 247 * 140 } ) = 135° 6'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12203.96 }{ 373.5 } = 32.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 140 }{ 2 * sin 15° 55'55" } = 255.02 ; ;




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