11 11 17 triangle

Obtuse isosceles triangle.

Sides: a = 11   b = 11   c = 17

Area: T = 59.3488020186
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 39.40105687537° = 39°24'2″ = 0.68876696519 rad
Angle ∠ B = β = 39.40105687537° = 39°24'2″ = 0.68876696519 rad
Angle ∠ C = γ = 101.1998862493° = 101°11'56″ = 1.76662533498 rad

Height: ha = 10.79105491247
Height: hb = 10.79105491247
Height: hc = 6.98221200219

Median: ma = 13.21993040664
Median: mb = 13.21993040664
Median: mc = 6.98221200219

Inradius: r = 3.04334882147
Circumradius: R = 8.66549899759

Vertex coordinates: A[17; 0] B[0; 0] C[8.5; 6.98221200219]
Centroid: CG[8.5; 2.32773733406]
Coordinates of the circumscribed circle: U[8.5; -1.6832869954]
Coordinates of the inscribed circle: I[8.5; 3.04334882147]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.5999431246° = 140°35'58″ = 0.68876696519 rad
∠ B' = β' = 140.5999431246° = 140°35'58″ = 0.68876696519 rad
∠ C' = γ' = 78.80111375075° = 78°48'4″ = 1.76662533498 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 = 11 ; ; b = 11 ; ; c = 17 ; ;

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

p = a+b+c = 11+11+17 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-11)(19.5-11)(19.5-17) } ; ; T = sqrt{ 3522.19 } = 59.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.35 }{ 11 } = 10.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.35 }{ 11 } = 10.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.35 }{ 17 } = 6.98 ; ;

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{ 11**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 39° 24'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 39° 24'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 101° 11'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.35 }{ 19.5 } = 3.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 39° 24'2" } = 8.66 ; ;




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