6 11 16 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 11   c = 16

Area: T = 21.82774483163
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 14.36215115629° = 14°21'41″ = 0.25106556623 rad
Angle ∠ B = β = 27.04881105464° = 27°2'53″ = 0.47220785855 rad
Angle ∠ C = γ = 138.5990377891° = 138°35'25″ = 2.41988584058 rad

Height: ha = 7.27658161054
Height: hb = 3.96986269666
Height: hc = 2.72884310395

Median: ma = 13.3987761007
Median: mb = 10.75987173957
Median: mc = 3.80878865529

Inradius: r = 1.32328756555
Circumradius: R = 12.09548631363

Vertex coordinates: A[16; 0] B[0; 0] C[5.344375; 2.72884310395]
Centroid: CG[7.11545833333; 0.90994770132]
Coordinates of the circumscribed circle: U[8; -9.07111473522]
Coordinates of the inscribed circle: I[5.5; 1.32328756555]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6388488437° = 165°38'19″ = 0.25106556623 rad
∠ B' = β' = 152.9521889454° = 152°57'7″ = 0.47220785855 rad
∠ C' = γ' = 41.41096221093° = 41°24'35″ = 2.41988584058 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 = 16 ; ;

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

p = a+b+c = 6+11+16 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-6)(16.5-11)(16.5-16) } ; ; T = sqrt{ 476.44 } = 21.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.83 }{ 6 } = 7.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.83 }{ 11 } = 3.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.83 }{ 16 } = 2.73 ; ;

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**2-16**2 }{ 2 * 11 * 16 } ) = 14° 21'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-6**2-16**2 }{ 2 * 6 * 16 } ) = 27° 2'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-6**2-11**2 }{ 2 * 11 * 6 } ) = 138° 35'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.83 }{ 16.5 } = 1.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 14° 21'41" } = 12.09 ; ;




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