6 11 13 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 11   c = 13

Area: T = 32.86333534503
Perimeter: p = 30
Semiperimeter: s = 15

Angle ∠ A = α = 27.36330618223° = 27°21'47″ = 0.47875755222 rad
Angle ∠ B = β = 57.42110296072° = 57°25'16″ = 1.00221860265 rad
Angle ∠ C = γ = 95.21659085705° = 95°12'57″ = 1.66218311048 rad

Height: ha = 10.95444511501
Height: hb = 5.97551551728
Height: hc = 5.05659005308

Median: ma = 11.66219037897
Median: mb = 8.5
Median: mc = 6.02107972894

Inradius: r = 2.191089023
Circumradius: R = 6.52770271436

Vertex coordinates: A[13; 0] B[0; 0] C[3.23107692308; 5.05659005308]
Centroid: CG[5.41102564103; 1.68553001769]
Coordinates of the circumscribed circle: U[6.5; -0.5933366104]
Coordinates of the inscribed circle: I[4; 2.191089023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.6376938178° = 152°38'13″ = 0.47875755222 rad
∠ B' = β' = 122.5798970393° = 122°34'44″ = 1.00221860265 rad
∠ C' = γ' = 84.78440914295° = 84°47'3″ = 1.66218311048 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 = 11 ; ; c = 13 ; ;

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

p = a+b+c = 6+11+13 = 30 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30 }{ 2 } = 15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15 * (15-6)(15-11)(15-13) } ; ; T = sqrt{ 1080 } = 32.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.86 }{ 6 } = 10.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.86 }{ 11 } = 5.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.86 }{ 13 } = 5.06 ; ;

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**2-11**2-13**2 }{ 2 * 11 * 13 } ) = 27° 21'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-6**2-13**2 }{ 2 * 6 * 13 } ) = 57° 25'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-6**2-11**2 }{ 2 * 11 * 6 } ) = 95° 12'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.86 }{ 15 } = 2.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 27° 21'47" } = 6.53 ; ;




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