6 7 11 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 7   c = 11

Area: T = 18.9743665961
Perimeter: p = 24
Semiperimeter: s = 12

Angle ∠ A = α = 29.52662652473° = 29°31'35″ = 0.51553305444 rad
Angle ∠ B = β = 35.09768012276° = 35°5'48″ = 0.61325547383 rad
Angle ∠ C = γ = 115.3776933525° = 115°22'37″ = 2.01437073709 rad

Height: ha = 6.32545553203
Height: hb = 5.42110474174
Height: hc = 3.45497574475

Median: ma = 8.71877978871
Median: mb = 8.1399410298
Median: mc = 3.5

Inradius: r = 1.58111388301
Circumradius: R = 6.08773844958

Vertex coordinates: A[11; 0] B[0; 0] C[4.90990909091; 3.45497574475]
Centroid: CG[5.3033030303; 1.15499191492]
Coordinates of the circumscribed circle: U[5.5; -2.60988790696]
Coordinates of the inscribed circle: I[5; 1.58111388301]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.4743734753° = 150°28'25″ = 0.51553305444 rad
∠ B' = β' = 144.9033198772° = 144°54'12″ = 0.61325547383 rad
∠ C' = γ' = 64.62330664748° = 64°37'23″ = 2.01437073709 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 = 7 ; ; c = 11 ; ;

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

p = a+b+c = 6+7+11 = 24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24 }{ 2 } = 12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12 * (12-6)(12-7)(12-11) } ; ; T = sqrt{ 360 } = 18.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.97 }{ 6 } = 6.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.97 }{ 7 } = 5.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.97 }{ 11 } = 3.45 ; ;

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**2-7**2-11**2 }{ 2 * 7 * 11 } ) = 29° 31'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-6**2-11**2 }{ 2 * 6 * 11 } ) = 35° 5'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-6**2-7**2 }{ 2 * 7 * 6 } ) = 115° 22'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.97 }{ 12 } = 1.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 29° 31'35" } = 6.09 ; ;




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