16 19 25 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 19   c = 25

Area: T = 151.9876841536
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 39.78876882825° = 39°47'16″ = 0.69444261623 rad
Angle ∠ B = β = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ C = γ = 90.7543913591° = 90°45'14″ = 1.58439546012 rad

Height: ha = 18.9988355192
Height: hb = 15.99986148985
Height: hc = 12.15989473229

Median: ma = 20.71223151772
Median: mb = 18.71549672722
Median: mc = 12.33989626793

Inradius: r = 5.06662280512
Circumradius: R = 12.50110822042

Vertex coordinates: A[25; 0] B[0; 0] C[10.4; 12.15989473229]
Centroid: CG[11.8; 4.0532982441]
Coordinates of the circumscribed circle: U[12.5; -0.16444879237]
Coordinates of the inscribed circle: I[11; 5.06662280512]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.2122311717° = 140°12'44″ = 0.69444261623 rad
∠ B' = β' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ C' = γ' = 89.2466086409° = 89°14'46″ = 1.58439546012 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 = 16 ; ; b = 19 ; ; c = 25 ; ;

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

p = a+b+c = 16+19+25 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-16)(30-19)(30-25) } ; ; T = sqrt{ 23100 } = 151.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.99 }{ 16 } = 19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.99 }{ 19 } = 16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.99 }{ 25 } = 12.16 ; ;

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{ 16**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 39° 47'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 49° 27'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-16**2-19**2 }{ 2 * 19 * 16 } ) = 90° 45'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.99 }{ 30 } = 5.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 39° 47'16" } = 12.5 ; ;




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