146.2 209.3 191.41 triangle

Acute scalene triangle.

Sides: a = 146.2   b = 209.3   c = 191.41

Area: T = 13533.8659896
Perimeter: p = 546.91
Semiperimeter: s = 273.455

Angle ∠ A = α = 42.50441679106° = 42°30'15″ = 0.74218376759 rad
Angle ∠ B = β = 75.29664635734° = 75°17'47″ = 1.31441712045 rad
Angle ∠ C = γ = 62.1999368516° = 62°11'58″ = 1.08655837733 rad

Height: ha = 185.1421722243
Height: hb = 129.3254987061
Height: hc = 141.4122255326

Median: ma = 186.7587942401
Median: mb = 134.3677003204
Median: mc = 153.0721937255

Inradius: r = 49.49220915543
Circumradius: R = 108.1933098008

Vertex coordinates: A[191.41; 0] B[0; 0] C[37.10881398569; 141.4122255326]
Centroid: CG[76.17327132856; 47.1377418442]
Coordinates of the circumscribed circle: U[95.705; 50.46108703012]
Coordinates of the inscribed circle: I[64.155; 49.49220915543]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.4965832089° = 137°29'45″ = 0.74218376759 rad
∠ B' = β' = 104.7043536427° = 104°42'13″ = 1.31441712045 rad
∠ C' = γ' = 117.8010631484° = 117°48'2″ = 1.08655837733 rad

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How did we calculate this triangle?

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

p = a+b+c = 146.2+209.3+191.41 = 546.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 546.91 }{ 2 } = 273.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 273.46 * (273.46-146.2)(273.46-209.3)(273.46-191.41) } ; ; T = sqrt{ 183165363.68 } = 13533.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13533.86 }{ 146.2 } = 185.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13533.86 }{ 209.3 } = 129.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13533.86 }{ 191.41 } = 141.41 ; ;

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{ 209.3**2+191.41**2-146.2**2 }{ 2 * 209.3 * 191.41 } ) = 42° 30'15" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 146.2**2+191.41**2-209.3**2 }{ 2 * 146.2 * 191.41 } ) = 75° 17'47" ; ;
 gamma = 180° - alpha - beta = 180° - 42° 30'15" - 75° 17'47" = 62° 11'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13533.86 }{ 273.46 } = 49.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 146.2 }{ 2 * sin 42° 30'15" } = 108.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 209.3**2+2 * 191.41**2 - 146.2**2 } }{ 2 } = 186.758 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 191.41**2+2 * 146.2**2 - 209.3**2 } }{ 2 } = 134.367 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 209.3**2+2 * 146.2**2 - 191.41**2 } }{ 2 } = 153.072 ; ;
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