11 25 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 25   c = 28

Area: T = 137.1711425596
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 93.96217737238° = 93°57'42″ = 1.64399423225 rad

Height: ha = 24.94402591992
Height: hb = 10.97437140477
Height: hc = 9.79879589711

Median: ma = 25.96663243452
Median: mb = 17.21219144781
Median: mc = 13.30441346957

Inradius: r = 4.28766070499
Circumradius: R = 14.03435349847

Vertex coordinates: A[28; 0] B[0; 0] C[5; 9.79879589711]
Centroid: CG[11; 3.26659863237]
Coordinates of the circumscribed circle: U[14; -0.97695896899]
Coordinates of the inscribed circle: I[7; 4.28766070499]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 86.03882262762° = 86°2'18″ = 1.64399423225 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 = 11 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 11+25+28 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-11)(32-25)(32-28) } ; ; T = sqrt{ 18816 } = 137.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.17 }{ 11 } = 24.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.17 }{ 25 } = 10.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.17 }{ 28 } = 9.8 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 25**2+28**2-11**2 }{ 2 * 25 * 28 } ) = 23° 4'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+28**2-25**2 }{ 2 * 11 * 28 } ) = 62° 57'52" ; ; gamma = 180° - alpha - beta = 180° - 23° 4'26" - 62° 57'52" = 93° 57'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.17 }{ 32 } = 4.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11 }{ 2 * sin 23° 4'26" } = 14.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 28**2 - 11**2 } }{ 2 } = 25.966 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 11**2 - 25**2 } }{ 2 } = 17.212 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 11**2 - 28**2 } }{ 2 } = 13.304 ; ;
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