141 145 49.82 triangle

Acute scalene triangle.

Sides: a = 141   b = 145   c = 49.82

Area: T = 3496.345464364
Perimeter: p = 335.82
Semiperimeter: s = 167.91

Angle ∠ A = α = 75.46548020732° = 75°27'53″ = 1.31771092655 rad
Angle ∠ B = β = 84.53549371046° = 84°32'6″ = 1.47554129854 rad
Angle ∠ C = γ = 200.0002608222° = 20°1″ = 0.34990704026 rad

Height: ha = 49.59435410446
Height: hb = 48.22554433606
Height: hc = 140.3599078428

Median: ma = 82.36105864476
Median: mb = 76.97657507271
Median: mc = 140.8287880407

Inradius: r = 20.82327302939
Circumradius: R = 72.83110567046

Vertex coordinates: A[49.82; 0] B[0; 0] C[13.42986672019; 140.3599078428]
Centroid: CG[21.08328890673; 46.7866359476]
Coordinates of the circumscribed circle: U[24.91; 68.43986931546]
Coordinates of the inscribed circle: I[22.91; 20.82327302939]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 104.5355197927° = 104°32'7″ = 1.31771092655 rad
∠ B' = β' = 95.46550628954° = 95°27'54″ = 1.47554129854 rad
∠ C' = γ' = 1609.999739178° = 159°59'59″ = 0.34990704026 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 = 141+145+49.82 = 335.82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 335.82 }{ 2 } = 167.91 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 167.91 * (167.91-141)(167.91-145)(167.91-49.82) } ; ; T = sqrt{ 12224425.87 } = 3496.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3496.34 }{ 141 } = 49.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3496.34 }{ 145 } = 48.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3496.34 }{ 49.82 } = 140.36 ; ;

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{ 145**2+49.82**2-141**2 }{ 2 * 145 * 49.82 } ) = 75° 27'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 141**2+49.82**2-145**2 }{ 2 * 141 * 49.82 } ) = 84° 32'6" ; ;
 gamma = 180° - alpha - beta = 180° - 75° 27'53" - 84° 32'6" = 20° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3496.34 }{ 167.91 } = 20.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 141 }{ 2 * sin 75° 27'53" } = 72.83 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 145**2+2 * 49.82**2 - 141**2 } }{ 2 } = 82.361 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 49.82**2+2 * 141**2 - 145**2 } }{ 2 } = 76.976 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 145**2+2 * 141**2 - 49.82**2 } }{ 2 } = 140.828 ; ;
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