9 19 25 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 19   c = 25

Area: T = 72.2330101066
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 17.70656342953° = 17°42'20″ = 0.30990216146 rad
Angle ∠ B = β = 39.94545051898° = 39°56'40″ = 0.69771631336 rad
Angle ∠ C = γ = 122.3549860515° = 122°20'59″ = 2.13554079053 rad

Height: ha = 16.05111335702
Height: hb = 7.60331685333
Height: hc = 5.77884080853

Median: ma = 21.74328149052
Median: mb = 16.21095650774
Median: mc = 8.04767384697

Inradius: r = 2.72656641912
Circumradius: R = 14.79664627521

Vertex coordinates: A[25; 0] B[0; 0] C[6.9; 5.77884080853]
Centroid: CG[10.63333333333; 1.92661360284]
Coordinates of the circumscribed circle: U[12.5; -7.91774055077]
Coordinates of the inscribed circle: I[7.5; 2.72656641912]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.2944365705° = 162°17'40″ = 0.30990216146 rad
∠ B' = β' = 140.055549481° = 140°3'20″ = 0.69771631336 rad
∠ C' = γ' = 57.65501394851° = 57°39'1″ = 2.13554079053 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 = 9 ; ; b = 19 ; ; c = 25 ; ;

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

p = a+b+c = 9+19+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-9)(26.5-19)(26.5-25) } ; ; T = sqrt{ 5217.19 } = 72.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72.23 }{ 9 } = 16.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72.23 }{ 19 } = 7.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72.23 }{ 25 } = 5.78 ; ;

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{ 9**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 17° 42'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-9**2-25**2 }{ 2 * 9 * 25 } ) = 39° 56'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-9**2-19**2 }{ 2 * 19 * 9 } ) = 122° 20'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72.23 }{ 26.5 } = 2.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 17° 42'20" } = 14.8 ; ;




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