14 18 25 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 18   c = 25

Area: T = 123.235529324
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 33.21102161481° = 33°12'37″ = 0.58796276171 rad
Angle ∠ B = β = 44.76550846713° = 44°45'54″ = 0.78112981174 rad
Angle ∠ C = γ = 102.0254699181° = 102°1'29″ = 1.78106669191 rad

Height: ha = 17.60550418915
Height: hb = 13.693281036
Height: hc = 9.85988234592

Median: ma = 20.62876513447
Median: mb = 18.15221348607
Median: mc = 10.18657743937

Inradius: r = 4.32440453768
Circumradius: R = 12.78804296853

Vertex coordinates: A[25; 0] B[0; 0] C[9.94; 9.85988234592]
Centroid: CG[11.64766666667; 3.28662744864]
Coordinates of the circumscribed circle: U[12.5; -2.66325895178]
Coordinates of the inscribed circle: I[10.5; 4.32440453768]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7989783852° = 146°47'23″ = 0.58796276171 rad
∠ B' = β' = 135.2354915329° = 135°14'6″ = 0.78112981174 rad
∠ C' = γ' = 77.97553008194° = 77°58'31″ = 1.78106669191 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 = 18 ; ; c = 25 ; ;

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

p = a+b+c = 14+18+25 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-14)(28.5-18)(28.5-25) } ; ; T = sqrt{ 15186.94 } = 123.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 123.24 }{ 14 } = 17.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 123.24 }{ 18 } = 13.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 123.24 }{ 25 } = 9.86 ; ;

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**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 33° 12'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 44° 45'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 102° 1'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 123.24 }{ 28.5 } = 4.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 33° 12'37" } = 12.78 ; ;




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