14 18 27 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 18   c = 27

Area: T = 114.6565734702
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 28.15334308856° = 28°9'12″ = 0.49113700647 rad
Angle ∠ B = β = 37.34772430261° = 37°20'50″ = 0.65218323573 rad
Angle ∠ C = γ = 114.4999326088° = 114°29'58″ = 1.99883902316 rad

Height: ha = 16.37993906717
Height: hb = 12.7439526078
Height: hc = 8.49330173853

Median: ma = 21.85217733834
Median: mb = 19.53220249846
Median: mc = 8.81875960443

Inradius: r = 3.88766350746
Circumradius: R = 14.83657167169

Vertex coordinates: A[27; 0] B[0; 0] C[11.13296296296; 8.49330173853]
Centroid: CG[12.71098765432; 2.83110057951]
Coordinates of the circumscribed circle: U[13.5; -6.15221126862]
Coordinates of the inscribed circle: I[11.5; 3.88766350746]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.8476569114° = 151°50'48″ = 0.49113700647 rad
∠ B' = β' = 142.6532756974° = 142°39'10″ = 0.65218323573 rad
∠ C' = γ' = 65.50106739117° = 65°30'2″ = 1.99883902316 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 = 27 ; ;

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

p = a+b+c = 14+18+27 = 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)(29.5-18)(29.5-27) } ; ; T = sqrt{ 13145.94 } = 114.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 114.66 }{ 14 } = 16.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 114.66 }{ 18 } = 12.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 114.66 }{ 27 } = 8.49 ; ;

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**2-27**2 }{ 2 * 18 * 27 } ) = 28° 9'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 37° 20'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 114° 29'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 114.66 }{ 29.5 } = 3.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 28° 9'12" } = 14.84 ; ;




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