10 20 25 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 20   c = 25

Area: T = 94.99217759598
Perimeter: p = 55
Semiperimeter: s = 27.5

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 = 18.9988355192
Height: hb = 9.4999177596
Height: hc = 7.59993420768

Median: ma = 22.07994021658
Median: mb = 16.2021851746
Median: mc = 9.68224583655

Inradius: r = 3.45442463985
Circumradius: R = 13.15990338992

Vertex coordinates: A[25; 0] B[0; 0] C[6.5; 7.59993420768]
Centroid: CG[10.5; 2.53331140256]
Coordinates of the circumscribed circle: U[12.5; -4.11221980935]
Coordinates of the inscribed circle: I[7.5; 3.45442463985]

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 = 10 ; ; b = 20 ; ; c = 25 ; ;

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

p = a+b+c = 10+20+25 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-10)(27.5-20)(27.5-25) } ; ; T = sqrt{ 9023.44 } = 94.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 94.99 }{ 10 } = 19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 94.99 }{ 20 } = 9.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 94.99 }{ 25 } = 7.6 ; ;

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{ 10**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 22° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-10**2-25**2 }{ 2 * 10 * 25 } ) = 49° 27'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-10**2-20**2 }{ 2 * 20 * 10 } ) = 108° 12'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 94.99 }{ 27.5 } = 3.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 22° 19'54" } = 13.16 ; ;




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