14 21 30 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 21   c = 30

Area: T = 131.4765995908
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 24.67695454829° = 24°40'10″ = 0.43105647936 rad
Angle ∠ B = β = 38.76112192061° = 38°45'40″ = 0.67765108972 rad
Angle ∠ C = γ = 116.5699235311° = 116°34'9″ = 2.03545169627 rad

Height: ha = 18.78222851297
Height: hb = 12.52215234198
Height: hc = 8.76550663939

Median: ma = 24.93299017246
Median: mb = 20.92224759529
Median: mc = 9.67695398029

Inradius: r = 4.04554152587
Circumradius: R = 16.77111222476

Vertex coordinates: A[30; 0] B[0; 0] C[10.91766666667; 8.76550663939]
Centroid: CG[13.63988888889; 2.9221688798]
Coordinates of the circumscribed circle: U[15; -7.50113693046]
Coordinates of the inscribed circle: I[11.5; 4.04554152587]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3330454517° = 155°19'50″ = 0.43105647936 rad
∠ B' = β' = 141.2398780794° = 141°14'20″ = 0.67765108972 rad
∠ C' = γ' = 63.4310764689° = 63°25'51″ = 2.03545169627 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 = 21 ; ; c = 30 ; ;

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

p = a+b+c = 14+21+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-14)(32.5-21)(32.5-30) } ; ; T = sqrt{ 17285.94 } = 131.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.48 }{ 14 } = 18.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.48 }{ 21 } = 12.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.48 }{ 30 } = 8.77 ; ;

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**2-21**2-30**2 }{ 2 * 21 * 30 } ) = 24° 40'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 38° 45'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-21**2 }{ 2 * 21 * 14 } ) = 116° 34'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.48 }{ 32.5 } = 4.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 24° 40'10" } = 16.77 ; ;




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