6 12 16 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 12   c = 16

Area: T = 30.57877697028
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 18.57333497187° = 18°34'24″ = 0.32441661057 rad
Angle ∠ B = β = 39.57112194572° = 39°34'16″ = 0.69106480686 rad
Angle ∠ C = γ = 121.8555430824° = 121°51'20″ = 2.12767784793 rad

Height: ha = 10.19325899009
Height: hb = 5.09662949505
Height: hc = 3.82222212129

Median: ma = 13.82202749611
Median: mb = 10.48880884817
Median: mc = 5.09990195136

Inradius: r = 1.79986923355
Circumradius: R = 9.41986071384

Vertex coordinates: A[16; 0] B[0; 0] C[4.625; 3.82222212129]
Centroid: CG[6.875; 1.27440737376]
Coordinates of the circumscribed circle: U[8; -4.97109315453]
Coordinates of the inscribed circle: I[5; 1.79986923355]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.4276650281° = 161°25'36″ = 0.32441661057 rad
∠ B' = β' = 140.4298780543° = 140°25'44″ = 0.69106480686 rad
∠ C' = γ' = 58.1454569176° = 58°8'40″ = 2.12767784793 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 = 6 ; ; b = 12 ; ; c = 16 ; ;

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

p = a+b+c = 6+12+16 = 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 * (17-6)(17-12)(17-16) } ; ; T = sqrt{ 935 } = 30.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.58 }{ 6 } = 10.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.58 }{ 12 } = 5.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.58 }{ 16 } = 3.82 ; ;

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{ 6**2-12**2-16**2 }{ 2 * 12 * 16 } ) = 18° 34'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-6**2-16**2 }{ 2 * 6 * 16 } ) = 39° 34'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-6**2-12**2 }{ 2 * 12 * 6 } ) = 121° 51'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.58 }{ 17 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 18° 34'24" } = 9.42 ; ;




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