15 25 27 triangle

Acute scalene triangle.

Sides: a = 15   b = 25   c = 27

Area: T = 185.0443744828
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 33.24989403241° = 33°14'56″ = 0.58803034815 rad
Angle ∠ B = β = 66.03553557996° = 66°2'7″ = 1.15325343814 rad
Angle ∠ C = γ = 80.71657038762° = 80°42'57″ = 1.40987547907 rad

Height: ha = 24.67224993104
Height: hb = 14.80334995862
Height: hc = 13.70769440613

Median: ma = 24.91548550066
Median: mb = 17.90994946886
Median: mc = 15.58804364509

Inradius: r = 5.52436938755
Circumradius: R = 13.67991978694

Vertex coordinates: A[27; 0] B[0; 0] C[6.09325925926; 13.70769440613]
Centroid: CG[11.03108641975; 4.56989813538]
Coordinates of the circumscribed circle: U[13.5; 2.20769105896]
Coordinates of the inscribed circle: I[8.5; 5.52436938755]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7511059676° = 146°45'4″ = 0.58803034815 rad
∠ B' = β' = 113.96546442° = 113°57'53″ = 1.15325343814 rad
∠ C' = γ' = 99.28442961238° = 99°17'3″ = 1.40987547907 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 = 15 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 15+25+27 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-15)(33.5-25)(33.5-27) } ; ; T = sqrt{ 34241.19 } = 185.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 185.04 }{ 15 } = 24.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 185.04 }{ 25 } = 14.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 185.04 }{ 27 } = 13.71 ; ;

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{ 15**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 33° 14'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-15**2-27**2 }{ 2 * 15 * 27 } ) = 66° 2'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-15**2-25**2 }{ 2 * 25 * 15 } ) = 80° 42'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 185.04 }{ 33.5 } = 5.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 33° 14'56" } = 13.68 ; ;




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