13 25 30 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 25   c = 30

Area: T = 160.3254670591
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 25.31110651555° = 25°18'40″ = 0.44217614242 rad
Angle ∠ B = β = 55.30333976437° = 55°18'12″ = 0.96552263764 rad
Angle ∠ C = γ = 99.38655372008° = 99°23'8″ = 1.7354604853 rad

Height: ha = 24.6655333937
Height: hb = 12.82659736473
Height: hc = 10.68883113727

Median: ma = 26.83774738006
Median: mb = 19.44986503388
Median: mc = 13.11548770486

Inradius: r = 4.7155431488
Circumradius: R = 15.20435241427

Vertex coordinates: A[30; 0] B[0; 0] C[7.4; 10.68883113727]
Centroid: CG[12.46766666667; 3.56327704576]
Coordinates of the circumscribed circle: U[15; -2.47993439371]
Coordinates of the inscribed circle: I[9; 4.7155431488]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.6898934845° = 154°41'20″ = 0.44217614242 rad
∠ B' = β' = 124.6976602356° = 124°41'48″ = 0.96552263764 rad
∠ C' = γ' = 80.61444627992° = 80°36'52″ = 1.7354604853 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 = 13 ; ; b = 25 ; ; c = 30 ; ;

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

p = a+b+c = 13+25+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-13)(34-25)(34-30) } ; ; T = sqrt{ 25704 } = 160.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 160.32 }{ 13 } = 24.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 160.32 }{ 25 } = 12.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 160.32 }{ 30 } = 10.69 ; ;

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{ 13**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 25° 18'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-13**2-30**2 }{ 2 * 13 * 30 } ) = 55° 18'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-13**2-25**2 }{ 2 * 25 * 13 } ) = 99° 23'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 160.32 }{ 34 } = 4.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 25° 18'40" } = 15.2 ; ;




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