32 60 68 triangle

Right scalene triangle.

Sides: a = 32   b = 60   c = 68

Area: T = 960
Perimeter: p = 160
Semiperimeter: s = 80

Angle ∠ A = α = 28.07224869359° = 28°4'21″ = 0.49899573263 rad
Angle ∠ B = β = 61.92875130641° = 61°55'39″ = 1.08108390005 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 60
Height: hb = 32
Height: hc = 28.23552941176

Median: ma = 62.0976698785
Median: mb = 43.86334243989
Median: mc = 34

Inradius: r = 12
Circumradius: R = 34

Vertex coordinates: A[68; 0] B[0; 0] C[15.05988235294; 28.23552941176]
Centroid: CG[27.68662745098; 9.41217647059]
Coordinates of the circumscribed circle: U[34; 0]
Coordinates of the inscribed circle: I[20; 12]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.9287513064° = 151°55'39″ = 0.49899573263 rad
∠ B' = β' = 118.0722486936° = 118°4'21″ = 1.08108390005 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 32+60+68 = 160 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 160 }{ 2 } = 80 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 80 * (80-32)(80-60)(80-68) } ; ; T = sqrt{ 921600 } = 960 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 960 }{ 32 } = 60 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 960 }{ 60 } = 32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 960 }{ 68 } = 28.24 ; ;

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{ 60**2+68**2-32**2 }{ 2 * 60 * 68 } ) = 28° 4'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 32**2+68**2-60**2 }{ 2 * 32 * 68 } ) = 61° 55'39" ; ;
gamma = 180° - alpha - beta = 180° - 28° 4'21" - 61° 55'39" = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 960 }{ 80 } = 12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 32 }{ 2 * sin 28° 4'21" } = 34 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 68**2 - 32**2 } }{ 2 } = 62.097 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 68**2+2 * 32**2 - 60**2 } }{ 2 } = 43.863 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 32**2 - 68**2 } }{ 2 } = 34 ; ;
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