14 15 25 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 15   c = 25

Area: T = 91.78223512447
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 29.30881092355° = 29°18'29″ = 0.51215230037 rad
Angle ∠ B = β = 31.63326096964° = 31°37'57″ = 0.55220931902 rad
Angle ∠ C = γ = 119.0599281068° = 119°3'33″ = 2.07879764597 rad

Height: ha = 13.11217644635
Height: hb = 12.23876468326
Height: hc = 7.34325880996

Median: ma = 19.39107194297
Median: mb = 18.82215302247
Median: mc = 7.36554599313

Inradius: r = 3.39993463424
Circumradius: R = 14.33001348538

Vertex coordinates: A[25; 0] B[0; 0] C[11.92; 7.34325880996]
Centroid: CG[12.30766666667; 2.44875293665]
Coordinates of the circumscribed circle: U[12.5; -6.94657797861]
Coordinates of the inscribed circle: I[12; 3.39993463424]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.6921890764° = 150°41'31″ = 0.51215230037 rad
∠ B' = β' = 148.3677390304° = 148°22'3″ = 0.55220931902 rad
∠ C' = γ' = 60.9410718932° = 60°56'27″ = 2.07879764597 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 = 14 ; ; b = 15 ; ; c = 25 ; ;

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

p = a+b+c = 14+15+25 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-14)(27-15)(27-25) } ; ; T = sqrt{ 8424 } = 91.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.78 }{ 14 } = 13.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.78 }{ 15 } = 12.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.78 }{ 25 } = 7.34 ; ;

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{ 14**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 29° 18'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 31° 37'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-15**2 }{ 2 * 15 * 14 } ) = 119° 3'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.78 }{ 27 } = 3.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 29° 18'29" } = 14.3 ; ;




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