14 16 27 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 16   c = 27

Area: T = 88.02552094573
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 24.04993983611° = 24°2'58″ = 0.42197411845 rad
Angle ∠ B = β = 27.75882438109° = 27°45'30″ = 0.48444727491 rad
Angle ∠ C = γ = 128.1922357828° = 128°11'32″ = 2.237737872 rad

Height: ha = 12.57550299225
Height: hb = 11.00331511822
Height: hc = 6.52203858857

Median: ma = 21.05994396887
Median: mb = 19.96224647777
Median: mc = 6.61443782777

Inradius: r = 3.08986038406
Circumradius: R = 17.1776897497

Vertex coordinates: A[27; 0] B[0; 0] C[12.38988888889; 6.52203858857]
Centroid: CG[13.13296296296; 2.17334619619]
Coordinates of the circumscribed circle: U[13.5; -10.62105370685]
Coordinates of the inscribed circle: I[12.5; 3.08986038406]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.9510601639° = 155°57'2″ = 0.42197411845 rad
∠ B' = β' = 152.2421756189° = 152°14'30″ = 0.48444727491 rad
∠ C' = γ' = 51.8087642172° = 51°48'28″ = 2.237737872 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 = 16 ; ; c = 27 ; ;

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

p = a+b+c = 14+16+27 = 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)(28.5-16)(28.5-27) } ; ; T = sqrt{ 7748.44 } = 88.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.03 }{ 14 } = 12.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.03 }{ 16 } = 11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.03 }{ 27 } = 6.52 ; ;

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**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 24° 2'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 27° 45'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-16**2 }{ 2 * 16 * 14 } ) = 128° 11'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.03 }{ 28.5 } = 3.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 24° 2'58" } = 17.18 ; ;




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