9 11 14 triangle

Acute scalene triangle.

Sides: a = 9   b = 11   c = 14

Area: T = 49.47772675074
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 39.98331214543° = 39°58'59″ = 0.69878371146 rad
Angle ∠ B = β = 51.75333801217° = 51°45'12″ = 0.90332668822 rad
Angle ∠ C = γ = 88.26334984241° = 88°15'49″ = 1.54404886568 rad

Height: ha = 10.9954948335
Height: hb = 8.99658668195
Height: hc = 7.06881810725

Median: ma = 11.75879760163
Median: mb = 10.40443260233
Median: mc = 7.21111025509

Inradius: r = 2.91104275004
Circumradius: R = 7.00332161729

Vertex coordinates: A[14; 0] B[0; 0] C[5.57114285714; 7.06881810725]
Centroid: CG[6.52438095238; 2.35660603575]
Coordinates of the circumscribed circle: U[7; 0.21222186719]
Coordinates of the inscribed circle: I[6; 2.91104275004]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.0176878546° = 140°1'1″ = 0.69878371146 rad
∠ B' = β' = 128.2476619878° = 128°14'48″ = 0.90332668822 rad
∠ C' = γ' = 91.73765015759° = 91°44'11″ = 1.54404886568 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 = 9 ; ; b = 11 ; ; c = 14 ; ;

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

p = a+b+c = 9+11+14 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-9)(17-11)(17-14) } ; ; T = sqrt{ 2448 } = 49.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.48 }{ 9 } = 10.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.48 }{ 11 } = 9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.48 }{ 14 } = 7.07 ; ;

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{ 9**2-11**2-14**2 }{ 2 * 11 * 14 } ) = 39° 58'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-9**2-14**2 }{ 2 * 9 * 14 } ) = 51° 45'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-9**2-11**2 }{ 2 * 11 * 9 } ) = 88° 15'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.48 }{ 17 } = 2.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 39° 58'59" } = 7 ; ;




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