80 80.5 66 triangle

Acute scalene triangle.

Sides: a = 80   b = 80.5   c = 66

Area: T = 2413.912230601
Perimeter: p = 226.5
Semiperimeter: s = 113.25

Angle ∠ A = α = 65.3243770709° = 65°19'26″ = 1.14401148787 rad
Angle ∠ B = β = 66.11551036176° = 66°6'54″ = 1.15439262434 rad
Angle ∠ C = γ = 48.56111256734° = 48°33'40″ = 0.84875515315 rad

Height: ha = 60.34878076502
Height: hb = 59.97329765468
Height: hc = 73.14988577578

Median: ma = 61.79109783059
Median: mb = 61.3022018727
Median: mc = 73.15113841291

Inradius: r = 21.31548989493
Circumradius: R = 44.02198261285

Vertex coordinates: A[66; 0] B[0; 0] C[32.39220454545; 73.14988577578]
Centroid: CG[32.79773484848; 24.38329525859]
Coordinates of the circumscribed circle: U[33; 29.1333230037]
Coordinates of the inscribed circle: I[32.75; 21.31548989493]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.6766229291° = 114°40'34″ = 1.14401148787 rad
∠ B' = β' = 113.8854896382° = 113°53'6″ = 1.15439262434 rad
∠ C' = γ' = 131.4398874327° = 131°26'20″ = 0.84875515315 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 = 80 ; ; b = 80.5 ; ; c = 66 ; ;

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

p = a+b+c = 80+80.5+66 = 226.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 226.5 }{ 2 } = 113.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 113.25 * (113.25-80)(113.25-80.5)(113.25-66) } ; ; T = sqrt{ 5826972.62 } = 2413.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2413.91 }{ 80 } = 60.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2413.91 }{ 80.5 } = 59.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2413.91 }{ 66 } = 73.15 ; ;

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{ 80.5**2+66**2-80**2 }{ 2 * 80.5 * 66 } ) = 65° 19'26" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 80**2+66**2-80.5**2 }{ 2 * 80 * 66 } ) = 66° 6'54" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 80**2+80.5**2-66**2 }{ 2 * 80 * 80.5 } ) = 48° 33'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2413.91 }{ 113.25 } = 21.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 80 }{ 2 * sin 65° 19'26" } = 44.02 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 80.5**2+2 * 66**2 - 80**2 } }{ 2 } = 61.791 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 66**2+2 * 80**2 - 80.5**2 } }{ 2 } = 61.302 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 80.5**2+2 * 80**2 - 66**2 } }{ 2 } = 73.151 ; ;
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