11 12 14 triangle

Acute scalene triangle.

Sides: a = 11   b = 12   c = 14

Area: T = 63.70658670767
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 49.32436272308° = 49°19'25″ = 0.86108596942 rad
Angle ∠ B = β = 55.82773636603° = 55°49'38″ = 0.97443713086 rad
Angle ∠ C = γ = 74.84990091089° = 74°50'56″ = 1.30663616508 rad

Height: ha = 11.5832884923
Height: hb = 10.61876445128
Height: hc = 9.10108381538

Median: ma = 11.82215904175
Median: mb = 11.06879718106
Median: mc = 9.13878334412

Inradius: r = 3.44435603825
Circumradius: R = 7.25220793013

Vertex coordinates: A[14; 0] B[0; 0] C[6.17985714286; 9.10108381538]
Centroid: CG[6.72661904762; 3.03436127179]
Coordinates of the circumscribed circle: U[7; 1.89554298174]
Coordinates of the inscribed circle: I[6.5; 3.44435603825]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.6766372769° = 130°40'35″ = 0.86108596942 rad
∠ B' = β' = 124.173263634° = 124°10'22″ = 0.97443713086 rad
∠ C' = γ' = 105.1510990891° = 105°9'4″ = 1.30663616508 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 = 11 ; ; b = 12 ; ; c = 14 ; ;

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

p = a+b+c = 11+12+14 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-11)(18.5-12)(18.5-14) } ; ; T = sqrt{ 4058.44 } = 63.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.71 }{ 11 } = 11.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.71 }{ 12 } = 10.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.71 }{ 14 } = 9.1 ; ;

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{ 11**2-12**2-14**2 }{ 2 * 12 * 14 } ) = 49° 19'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-11**2-14**2 }{ 2 * 11 * 14 } ) = 55° 49'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-11**2-12**2 }{ 2 * 12 * 11 } ) = 74° 50'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.71 }{ 18.5 } = 3.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 49° 19'25" } = 7.25 ; ;




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