11 17 25 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 17   c = 25

Area: T = 76.50661272056
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 21.10219668232° = 21°6'7″ = 0.36882987997 rad
Angle ∠ B = β = 33.80877628245° = 33°48'28″ = 0.5990056774 rad
Angle ∠ C = γ = 125.0990270352° = 125°5'25″ = 2.18332370799 rad

Height: ha = 13.91102049465
Height: hb = 9.00107208477
Height: hc = 6.12204901764

Median: ma = 20.65879282601
Median: mb = 17.3422145196
Median: mc = 6.98221200219

Inradius: r = 2.88770236681
Circumradius: R = 15.27765542145

Vertex coordinates: A[25; 0] B[0; 0] C[9.14; 6.12204901764]
Centroid: CG[11.38; 2.04401633921]
Coordinates of the circumscribed circle: U[12.5; -8.78219763533]
Coordinates of the inscribed circle: I[9.5; 2.88770236681]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.8988033177° = 158°53'53″ = 0.36882987997 rad
∠ B' = β' = 146.1922237176° = 146°11'32″ = 0.5990056774 rad
∠ C' = γ' = 54.91097296477° = 54°54'35″ = 2.18332370799 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 = 17 ; ; c = 25 ; ;

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

p = a+b+c = 11+17+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-11)(26.5-17)(26.5-25) } ; ; T = sqrt{ 5853.19 } = 76.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.51 }{ 11 } = 13.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.51 }{ 17 } = 9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.51 }{ 25 } = 6.12 ; ;

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{ 11**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 21° 6'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 33° 48'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-17**2 }{ 2 * 17 * 11 } ) = 125° 5'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.51 }{ 26.5 } = 2.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 6'7" } = 15.28 ; ;




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