3 11 11 triangle

Acute isosceles triangle.

Sides: a = 3   b = 11   c = 11

Area: T = 16.34658710383
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 15.67549595262° = 15°40'30″ = 0.27435796538 rad
Angle ∠ B = β = 82.16325202369° = 82°9'45″ = 1.43440064999 rad
Angle ∠ C = γ = 82.16325202369° = 82°9'45″ = 1.43440064999 rad

Height: ha = 10.89772473589
Height: hb = 2.97219765524
Height: hc = 2.97219765524

Median: ma = 10.89772473589
Median: mb = 5.89549130613
Median: mc = 5.89549130613

Inradius: r = 1.30876696831
Circumradius: R = 5.55218607597

Vertex coordinates: A[11; 0] B[0; 0] C[0.40990909091; 2.97219765524]
Centroid: CG[3.8033030303; 0.99106588508]
Coordinates of the circumscribed circle: U[5.5; 0.75770719218]
Coordinates of the inscribed circle: I[1.5; 1.30876696831]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.3255040474° = 164°19'30″ = 0.27435796538 rad
∠ B' = β' = 97.83774797631° = 97°50'15″ = 1.43440064999 rad
∠ C' = γ' = 97.83774797631° = 97°50'15″ = 1.43440064999 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 = 3 ; ; b = 11 ; ; c = 11 ; ;

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

p = a+b+c = 3+11+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 * (12.5-3)(12.5-11)(12.5-11) } ; ; T = sqrt{ 267.19 } = 16.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.35 }{ 3 } = 10.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.35 }{ 11 } = 2.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.35 }{ 11 } = 2.97 ; ;

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{ 3**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 15° 40'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-3**2-11**2 }{ 2 * 3 * 11 } ) = 82° 9'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-3**2-11**2 }{ 2 * 11 * 3 } ) = 82° 9'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.35 }{ 12.5 } = 1.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 15° 40'30" } = 5.55 ; ;




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