120 160 198.5 triangle

Acute scalene triangle.

Sides: a = 120   b = 160   c = 198.5

Area: T = 9598.837682712
Perimeter: p = 478.5
Semiperimeter: s = 239.25

Angle ∠ A = α = 37.19900483617° = 37°11'24″ = 0.64990887929 rad
Angle ∠ B = β = 53.70218770419° = 53°42'7″ = 0.93772745689 rad
Angle ∠ C = γ = 89.10880745964° = 89°6'29″ = 1.55552292918 rad

Height: ha = 159.9810613785
Height: hb = 119.9855460339
Height: hc = 96.714372118

Median: ma = 170.0033308791
Median: mb = 143.1822139249
Median: mc = 100.7444416719

Inradius: r = 40.12105301029
Circumradius: R = 99.26220269686

Vertex coordinates: A[198.5; 0] B[0; 0] C[71.03884130982; 96.714372118]
Centroid: CG[89.84661376994; 32.238790706]
Coordinates of the circumscribed circle: U[99.25; 1.5455153037]
Coordinates of the inscribed circle: I[79.25; 40.12105301029]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.8109951638° = 142°48'36″ = 0.64990887929 rad
∠ B' = β' = 126.2988122958° = 126°17'53″ = 0.93772745689 rad
∠ C' = γ' = 90.89219254036° = 90°53'31″ = 1.55552292918 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 = 120 ; ; b = 160 ; ; c = 198.5 ; ;

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

p = a+b+c = 120+160+198.5 = 478.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 478.5 }{ 2 } = 239.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 239.25 * (239.25-120)(239.25-160)(239.25-198.5) } ; ; T = sqrt{ 92137668.43 } = 9598.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9598.84 }{ 120 } = 159.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9598.84 }{ 160 } = 119.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9598.84 }{ 198.5 } = 96.71 ; ;

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{ 120**2-160**2-198.5**2 }{ 2 * 160 * 198.5 } ) = 37° 11'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 160**2-120**2-198.5**2 }{ 2 * 120 * 198.5 } ) = 53° 42'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 198.5**2-120**2-160**2 }{ 2 * 160 * 120 } ) = 89° 6'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9598.84 }{ 239.25 } = 40.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 120 }{ 2 * sin 37° 11'24" } = 99.26 ; ;




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