4 5 7 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 5   c = 7

Area: T = 9.79879589711
Perimeter: p = 16
Semiperimeter: s = 8

Angle ∠ A = α = 34.048773237° = 34°2'52″ = 0.59442450327 rad
Angle ∠ B = β = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ C = γ = 101.5376959033° = 101°32'13″ = 1.77221542476 rad

Height: ha = 4.89989794856
Height: hb = 3.91991835885
Height: hc = 2.79994168489

Median: ma = 5.74545626465
Median: mb = 5.1233475383
Median: mc = 2.87222813233

Inradius: r = 1.22547448714
Circumradius: R = 3.57221725416

Vertex coordinates: A[7; 0] B[0; 0] C[2.85771428571; 2.79994168489]
Centroid: CG[3.28657142857; 0.93331389496]
Coordinates of the circumscribed circle: U[3.5; -0.71444345083]
Coordinates of the inscribed circle: I[3; 1.22547448714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.952226763° = 145°57'8″ = 0.59442450327 rad
∠ B' = β' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ C' = γ' = 78.46330409672° = 78°27'47″ = 1.77221542476 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 = 4 ; ; b = 5 ; ; c = 7 ; ;

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

p = a+b+c = 4+5+7 = 16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16 }{ 2 } = 8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8 * (8-4)(8-5)(8-7) } ; ; T = sqrt{ 96 } = 9.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.8 }{ 4 } = 4.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.8 }{ 5 } = 3.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.8 }{ 7 } = 2.8 ; ;

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{ 4**2-5**2-7**2 }{ 2 * 5 * 7 } ) = 34° 2'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5**2-4**2-7**2 }{ 2 * 4 * 7 } ) = 44° 24'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-4**2-5**2 }{ 2 * 5 * 4 } ) = 101° 32'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.8 }{ 8 } = 1.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 34° 2'52" } = 3.57 ; ;




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