2 4 5 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 4   c = 5

Area: T = 3.87996710384
Perimeter: p = 11
Semiperimeter: s = 5.5

Angle ∠ A = α = 22.33216450092° = 22°19'54″ = 0.39897607328 rad
Angle ∠ B = β = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ C = γ = 108.2109956864° = 108°12'36″ = 1.88986200307 rad

Height: ha = 3.87996710384
Height: hb = 1.98998355192
Height: hc = 1.52198684154

Median: ma = 4.41658804332
Median: mb = 3.24403703492
Median: mc = 1.93664916731

Inradius: r = 0.69108492797
Circumradius: R = 2.63218067798

Vertex coordinates: A[5; 0] B[0; 0] C[1.3; 1.52198684154]
Centroid: CG[2.1; 0.50766228051]
Coordinates of the circumscribed circle: U[2.5; -0.82224396187]
Coordinates of the inscribed circle: I[1.5; 0.69108492797]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6688354991° = 157°40'6″ = 0.39897607328 rad
∠ B' = β' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ C' = γ' = 71.79900431357° = 71°47'24″ = 1.88986200307 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 = 2 ; ; b = 4 ; ; c = 5 ; ;

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

p = a+b+c = 2+4+5 = 11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11 }{ 2 } = 5.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.5 * (5.5-2)(5.5-4)(5.5-5) } ; ; T = sqrt{ 14.44 } = 3.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.8 }{ 2 } = 3.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.8 }{ 4 } = 1.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.8 }{ 5 } = 1.52 ; ;

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{ 2**2-4**2-5**2 }{ 2 * 4 * 5 } ) = 22° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-2**2-5**2 }{ 2 * 2 * 5 } ) = 49° 27'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5**2-2**2-4**2 }{ 2 * 4 * 2 } ) = 108° 12'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.8 }{ 5.5 } = 0.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 22° 19'54" } = 2.63 ; ;




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