12 19 25 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 19   c = 25

Area: T = 109.9821816679
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 27.58661197531° = 27°35'10″ = 0.48114686175 rad
Angle ∠ B = β = 47.15663569564° = 47°9'23″ = 0.82330336921 rad
Angle ∠ C = γ = 105.258752329° = 105°15'27″ = 1.83770903439 rad

Height: ha = 18.33303027798
Height: hb = 11.57770333346
Height: hc = 8.79985453343

Median: ma = 21.37875583264
Median: mb = 17.15437167984
Median: mc = 9.81107084352

Inradius: r = 3.92879220242
Circumradius: R = 12.95766872328

Vertex coordinates: A[25; 0] B[0; 0] C[8.16; 8.79985453343]
Centroid: CG[11.05333333333; 2.93328484448]
Coordinates of the circumscribed circle: U[12.5; -3.41096545349]
Coordinates of the inscribed circle: I[9; 3.92879220242]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.4143880247° = 152°24'50″ = 0.48114686175 rad
∠ B' = β' = 132.8443643044° = 132°50'37″ = 0.82330336921 rad
∠ C' = γ' = 74.74224767095° = 74°44'33″ = 1.83770903439 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 = 12 ; ; b = 19 ; ; c = 25 ; ;

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

p = a+b+c = 12+19+25 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-12)(28-19)(28-25) } ; ; T = sqrt{ 12096 } = 109.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 109.98 }{ 12 } = 18.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 109.98 }{ 19 } = 11.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 109.98 }{ 25 } = 8.8 ; ;

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{ 12**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 27° 35'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-12**2-25**2 }{ 2 * 12 * 25 } ) = 47° 9'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-12**2-19**2 }{ 2 * 19 * 12 } ) = 105° 15'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 109.98 }{ 28 } = 3.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 27° 35'10" } = 12.96 ; ;




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