14 18 30 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 18   c = 30

Area: T = 82.77107677867
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 17.85219455267° = 17°51'7″ = 0.31215752273 rad
Angle ∠ B = β = 23.2132754908° = 23°12'46″ = 0.40551390016 rad
Angle ∠ C = γ = 138.9355299565° = 138°56'7″ = 2.42548784247 rad

Height: ha = 11.82443953981
Height: hb = 9.19767519763
Height: hc = 5.51880511858

Median: ma = 23.72876210354
Median: mb = 21.6110182785
Median: mc = 5.91660797831

Inradius: r = 2.67700247673
Circumradius: R = 22.83441484625

Vertex coordinates: A[30; 0] B[0; 0] C[12.86766666667; 5.51880511858]
Centroid: CG[14.28988888889; 1.83993503953]
Coordinates of the circumscribed circle: U[15; -17.21662230472]
Coordinates of the inscribed circle: I[13; 2.67700247673]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.1488054473° = 162°8'53″ = 0.31215752273 rad
∠ B' = β' = 156.7877245092° = 156°47'14″ = 0.40551390016 rad
∠ C' = γ' = 41.06547004347° = 41°3'53″ = 2.42548784247 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 = 30 ; ;

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

p = a+b+c = 14+18+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-14)(31-18)(31-30) } ; ; T = sqrt{ 6851 } = 82.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 82.77 }{ 14 } = 11.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 82.77 }{ 18 } = 9.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 82.77 }{ 30 } = 5.52 ; ;

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**2-30**2 }{ 2 * 18 * 30 } ) = 17° 51'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 23° 12'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 138° 56'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 82.77 }{ 31 } = 2.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 17° 51'7" } = 22.83 ; ;




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