10 17 25 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 17   c = 25

Area: T = 61.18882341631
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 16.73549440407° = 16°44'6″ = 0.29220798736 rad
Angle ∠ B = β = 29.30881092355° = 29°18'29″ = 0.51215230037 rad
Angle ∠ C = γ = 133.9576946724° = 133°57'25″ = 2.33879897762 rad

Height: ha = 12.23876468326
Height: hb = 7.19986157839
Height: hc = 4.8955058733

Median: ma = 20.78546096908
Median: mb = 17.03767250374
Median: mc = 6.18546584384

Inradius: r = 2.35333936217
Circumradius: R = 17.36444494654

Vertex coordinates: A[25; 0] B[0; 0] C[8.72; 4.8955058733]
Centroid: CG[11.24; 1.63216862443]
Coordinates of the circumscribed circle: U[12.5; -12.05329708054]
Coordinates of the inscribed circle: I[9; 2.35333936217]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.2655055959° = 163°15'54″ = 0.29220798736 rad
∠ B' = β' = 150.6921890764° = 150°41'31″ = 0.51215230037 rad
∠ C' = γ' = 46.04330532762° = 46°2'35″ = 2.33879897762 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 = 10 ; ; b = 17 ; ; c = 25 ; ;

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

p = a+b+c = 10+17+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-10)(26-17)(26-25) } ; ; T = sqrt{ 3744 } = 61.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.19 }{ 10 } = 12.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.19 }{ 17 } = 7.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.19 }{ 25 } = 4.9 ; ;

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{ 17**2+25**2-10**2 }{ 2 * 17 * 25 } ) = 16° 44'6" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+25**2-17**2 }{ 2 * 10 * 25 } ) = 29° 18'29" ; ; gamma = 180° - alpha - beta = 180° - 16° 44'6" - 29° 18'29" = 133° 57'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.19 }{ 26 } = 2.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 16° 44'6" } = 17.36 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 25**2 - 10**2 } }{ 2 } = 20.785 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 10**2 - 17**2 } }{ 2 } = 17.037 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 10**2 - 25**2 } }{ 2 } = 6.185 ; ;
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