11 11 18 triangle

Obtuse isosceles triangle.

Sides: a = 11   b = 11   c = 18

Area: T = 56.9210997883
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 35.09768012276° = 35°5'48″ = 0.61325547383 rad
Angle ∠ B = β = 35.09768012276° = 35°5'48″ = 0.61325547383 rad
Angle ∠ C = γ = 109.8066397545° = 109°48'23″ = 1.91664831769 rad

Height: ha = 10.34992723424
Height: hb = 10.34992723424
Height: hc = 6.32545553203

Median: ma = 13.86554246239
Median: mb = 13.86554246239
Median: mc = 6.32545553203

Inradius: r = 2.84660498942
Circumradius: R = 9.5665889922

Vertex coordinates: A[18; 0] B[0; 0] C[9; 6.32545553203]
Centroid: CG[9; 2.10881851068]
Coordinates of the circumscribed circle: U[9; -3.24113346017]
Coordinates of the inscribed circle: I[9; 2.84660498942]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.9033198772° = 144°54'12″ = 0.61325547383 rad
∠ B' = β' = 144.9033198772° = 144°54'12″ = 0.61325547383 rad
∠ C' = γ' = 70.19436024552° = 70°11'37″ = 1.91664831769 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 = 18 ; ;

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

p = a+b+c = 11+11+18 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-11)(20-11)(20-18) } ; ; T = sqrt{ 3240 } = 56.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 56.92 }{ 11 } = 10.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 56.92 }{ 11 } = 10.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 56.92 }{ 18 } = 6.32 ; ;

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**2-18**2 }{ 2 * 11 * 18 } ) = 35° 5'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 35° 5'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 109° 48'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 56.92 }{ 20 } = 2.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 35° 5'48" } = 9.57 ; ;




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