65 55 10.62 triangle

Obtuse scalene triangle.

Sides: a = 65   b = 55   c = 10.62

Area: T = 106.8454945808
Perimeter: p = 130.62
Semiperimeter: s = 65.31

Angle ∠ A = α = 158.5440423524° = 158°32'26″ = 2.7677052388 rad
Angle ∠ B = β = 18.03327704912° = 18°1'58″ = 0.31547312183 rad
Angle ∠ C = γ = 3.42768059845° = 3°25'37″ = 0.06598090473 rad

Height: ha = 3.28875367941
Height: hb = 3.88552707567
Height: hc = 20.1211458721

Median: ma = 22.64216033001
Median: mb = 37.5855132699
Median: mc = 59.97333599192

Inradius: r = 1.63659660972
Circumradius: R = 88.83655076432

Vertex coordinates: A[10.62; 0] B[0; 0] C[61.80771751412; 20.1211458721]
Centroid: CG[24.14223917137; 6.7077152907]
Coordinates of the circumscribed circle: U[5.31; 88.67766672707]
Coordinates of the inscribed circle: I[10.31; 1.63659660972]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 21.46595764758° = 21°27'34″ = 2.7677052388 rad
∠ B' = β' = 161.9677229509° = 161°58'2″ = 0.31547312183 rad
∠ C' = γ' = 176.5733194015° = 176°34'23″ = 0.06598090473 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 = 65+55+10.62 = 130.62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 130.62 }{ 2 } = 65.31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 65.31 * (65.31-65)(65.31-55)(65.31-10.62) } ; ; T = sqrt{ 11415.84 } = 106.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 106.84 }{ 65 } = 3.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 106.84 }{ 55 } = 3.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 106.84 }{ 10.62 } = 20.12 ; ;

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{ 55**2+10.62**2-65**2 }{ 2 * 55 * 10.62 } ) = 158° 32'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 65**2+10.62**2-55**2 }{ 2 * 65 * 10.62 } ) = 18° 1'58" ; ; gamma = 180° - alpha - beta = 180° - 158° 32'26" - 18° 1'58" = 3° 25'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 106.84 }{ 65.31 } = 1.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 65 }{ 2 * sin 158° 32'26" } = 88.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 10.62**2 - 65**2 } }{ 2 } = 22.642 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.62**2+2 * 65**2 - 55**2 } }{ 2 } = 37.585 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 65**2 - 10.62**2 } }{ 2 } = 59.973 ; ;
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