98 122 201 triangle

Obtuse scalene triangle.

Sides: a = 98   b = 122   c = 201

Area: T = 4462.064352907
Perimeter: p = 421
Semiperimeter: s = 210.5

Angle ∠ A = α = 21.34113355003° = 21°20'29″ = 0.37224765713 rad
Angle ∠ B = β = 26.93993686769° = 26°56'22″ = 0.47701806818 rad
Angle ∠ C = γ = 131.7199295823° = 131°43'9″ = 2.29989354005 rad

Height: ha = 91.06325210015
Height: hb = 73.14985824439
Height: hc = 44.39986420803

Median: ma = 158.8765737606
Median: mb = 145.882180147
Median: mc = 46.30106479436

Inradius: r = 21.19774514445
Circumradius: R = 134.6443757554

Vertex coordinates: A[201; 0] B[0; 0] C[87.36656716418; 44.39986420803]
Centroid: CG[96.12218905473; 14.87995473601]
Coordinates of the circumscribed circle: U[100.5; -89.60329656223]
Coordinates of the inscribed circle: I[88.5; 21.19774514445]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.65986645° = 158°39'31″ = 0.37224765713 rad
∠ B' = β' = 153.0610631323° = 153°3'38″ = 0.47701806818 rad
∠ C' = γ' = 48.28107041772° = 48°16'51″ = 2.29989354005 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 = 98 ; ; b = 122 ; ; c = 201 ; ;

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

p = a+b+c = 98+122+201 = 421 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 421 }{ 2 } = 210.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 210.5 * (210.5-98)(210.5-122)(210.5-201) } ; ; T = sqrt{ 19910010.94 } = 4462.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4462.06 }{ 98 } = 91.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4462.06 }{ 122 } = 73.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4462.06 }{ 201 } = 44.4 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 122**2+201**2-98**2 }{ 2 * 122 * 201 } ) = 21° 20'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 98**2+201**2-122**2 }{ 2 * 98 * 201 } ) = 26° 56'22" ; ;
 gamma = 180° - alpha - beta = 180° - 21° 20'29" - 26° 56'22" = 131° 43'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4462.06 }{ 210.5 } = 21.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 98 }{ 2 * sin 21° 20'29" } = 134.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 122**2+2 * 201**2 - 98**2 } }{ 2 } = 158.876 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 201**2+2 * 98**2 - 122**2 } }{ 2 } = 145.882 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 122**2+2 * 98**2 - 201**2 } }{ 2 } = 46.301 ; ;
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