7 7 11 triangle

Obtuse isosceles triangle.

Sides: a = 7   b = 7   c = 11

Area: T = 23.81656986041
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ B = β = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ C = γ = 103.5743578597° = 103°34'25″ = 1.80876999646 rad

Height: ha = 6.80444853154
Height: hb = 6.80444853154
Height: hc = 4.33301270189

Median: ma = 8.52993610546
Median: mb = 8.52993610546
Median: mc = 4.33301270189

Inradius: r = 1.90552558883
Circumradius: R = 5.65880326381

Vertex coordinates: A[11; 0] B[0; 0] C[5.5; 4.33301270189]
Centroid: CG[5.5; 1.4433375673]
Coordinates of the circumscribed circle: U[5.5; -1.32879056191]
Coordinates of the inscribed circle: I[5.5; 1.90552558883]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ B' = β' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ C' = γ' = 76.42664214035° = 76°25'35″ = 1.80876999646 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 = 7 ; ; b = 7 ; ; c = 11 ; ;

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

p = a+b+c = 7+7+11 = 25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25 }{ 2 } = 12.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.5 * (12.5-7)(12.5-7)(12.5-11) } ; ; T = sqrt{ 567.19 } = 23.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.82 }{ 7 } = 6.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.82 }{ 7 } = 6.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.82 }{ 11 } = 4.33 ; ;

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{ 7**2-7**2-11**2 }{ 2 * 7 * 11 } ) = 38° 12'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-7**2-11**2 }{ 2 * 7 * 11 } ) = 38° 12'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 103° 34'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.82 }{ 12.5 } = 1.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 38° 12'48" } = 5.66 ; ;




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