40 42 58 triangle

Right scalene triangle.

Sides: a = 40   b = 42   c = 58

Area: T = 840
Perimeter: p = 140
Semiperimeter: s = 70

Angle ∠ A = α = 43.60328189727° = 43°36'10″ = 0.76110127542 rad
Angle ∠ B = β = 46.39771810273° = 46°23'50″ = 0.81097835726 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 42
Height: hb = 40
Height: hc = 28.96655172414

Median: ma = 46.51988133985
Median: mb = 45.17774279923
Median: mc = 29

Inradius: r = 12
Circumradius: R = 29

Vertex coordinates: A[58; 0] B[0; 0] C[27.58662068966; 28.96655172414]
Centroid: CG[28.52987356322; 9.65551724138]
Coordinates of the circumscribed circle: U[29; 0]
Coordinates of the inscribed circle: I[28; 12]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.3977181027° = 136°23'50″ = 0.76110127542 rad
∠ B' = β' = 133.6032818973° = 133°36'10″ = 0.81097835726 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

a = 40 ; ; b = 42 ; ; c = 58 ; ;

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

p = a+b+c = 40+42+58 = 140 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 140 }{ 2 } = 70 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 70 * (70-40)(70-42)(70-58) } ; ; T = sqrt{ 705600 } = 840 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 840 }{ 40 } = 42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 840 }{ 42 } = 40 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 840 }{ 58 } = 28.97 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 40**2-42**2-58**2 }{ 2 * 42 * 58 } ) = 43° 36'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 42**2-40**2-58**2 }{ 2 * 40 * 58 } ) = 46° 23'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 58**2-40**2-42**2 }{ 2 * 42 * 40 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 840 }{ 70 } = 12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 43° 36'10" } = 29 ; ;




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