19 25 28 triangle

Acute scalene triangle.

Sides: a = 19   b = 25   c = 28

Area: T = 232.069895527
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 41.53332182997° = 41°32' = 0.72548914083 rad
Angle ∠ B = β = 60.74333959328° = 60°44'36″ = 1.06601722579 rad
Angle ∠ C = γ = 77.72333857675° = 77°43'24″ = 1.35765289874 rad

Height: ha = 24.4288311081
Height: hb = 18.56655164216
Height: hc = 16.57663539478

Median: ma = 24.78440674628
Median: mb = 20.40222057631
Median: mc = 17.23436879396

Inradius: r = 6.44663598686
Circumradius: R = 14.32876380769

Vertex coordinates: A[28; 0] B[0; 0] C[9.28657142857; 16.57663539478]
Centroid: CG[12.42985714286; 5.52554513159]
Coordinates of the circumscribed circle: U[14; 3.04765083069]
Coordinates of the inscribed circle: I[11; 6.44663598686]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.46767817° = 138°28' = 0.72548914083 rad
∠ B' = β' = 119.2576604067° = 119°15'24″ = 1.06601722579 rad
∠ C' = γ' = 102.2776614232° = 102°16'36″ = 1.35765289874 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 = 19 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 19+25+28 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-19)(36-25)(36-28) } ; ; T = sqrt{ 53856 } = 232.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 232.07 }{ 19 } = 24.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 232.07 }{ 25 } = 18.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 232.07 }{ 28 } = 16.58 ; ;

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{ 19**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 41° 32' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 60° 44'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-19**2-25**2 }{ 2 * 25 * 19 } ) = 77° 43'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 232.07 }{ 36 } = 6.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 41° 32' } = 14.33 ; ;




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