14 20 25 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 20   c = 25

Area: T = 139.812215076
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 34.0043849551° = 34°14″ = 0.5933479133 rad
Angle ∠ B = β = 53.02877198019° = 53°1'40″ = 0.92655083054 rad
Angle ∠ C = γ = 92.9688430647° = 92°58'6″ = 1.62326052152 rad

Height: ha = 19.97331643942
Height: hb = 13.9811215076
Height: hc = 11.18549720608

Median: ma = 21.52990501416
Median: mb = 17.62110101867
Median: mc = 11.90658808998

Inradius: r = 4.7399394941
Circumradius: R = 12.51767947885

Vertex coordinates: A[25; 0] B[0; 0] C[8.42; 11.18549720608]
Centroid: CG[11.14; 3.72883240203]
Coordinates of the circumscribed circle: U[12.5; -0.64881911587]
Coordinates of the inscribed circle: I[9.5; 4.7399394941]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.9966150449° = 145°59'46″ = 0.5933479133 rad
∠ B' = β' = 126.9722280198° = 126°58'20″ = 0.92655083054 rad
∠ C' = γ' = 87.0321569353° = 87°1'54″ = 1.62326052152 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 = 20 ; ; c = 25 ; ;

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

p = a+b+c = 14+20+25 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-14)(29.5-20)(29.5-25) } ; ; T = sqrt{ 19547.44 } = 139.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.81 }{ 14 } = 19.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.81 }{ 20 } = 13.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.81 }{ 25 } = 11.18 ; ;

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**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 34° 14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 53° 1'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-20**2 }{ 2 * 20 * 14 } ) = 92° 58'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.81 }{ 29.5 } = 4.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 34° 14" } = 12.52 ; ;




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