11 30 30 triangle

Acute isosceles triangle.

Sides: a = 11   b = 30   c = 30

Area: T = 162.2033383134
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 21.12879551781° = 21°7'41″ = 0.36987523821 rad
Angle ∠ B = β = 79.43660224109° = 79°26'10″ = 1.38664201358 rad
Angle ∠ C = γ = 79.43660224109° = 79°26'10″ = 1.38664201358 rad

Height: ha = 29.49215242061
Height: hb = 10.81435588756
Height: hc = 10.81435588756

Median: ma = 29.49215242061
Median: mb = 16.89767452487
Median: mc = 16.89767452487

Inradius: r = 4.5699109384
Circumradius: R = 15.25986213196

Vertex coordinates: A[30; 0] B[0; 0] C[2.01766666667; 10.81435588756]
Centroid: CG[10.67222222222; 3.60545196252]
Coordinates of the circumscribed circle: U[15; 2.79774139086]
Coordinates of the inscribed circle: I[5.5; 4.5699109384]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.8722044822° = 158°52'19″ = 0.36987523821 rad
∠ B' = β' = 100.5643977589° = 100°33'50″ = 1.38664201358 rad
∠ C' = γ' = 100.5643977589° = 100°33'50″ = 1.38664201358 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 = 30 ; ; c = 30 ; ;

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

p = a+b+c = 11+30+30 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-11)(35.5-30)(35.5-30) } ; ; T = sqrt{ 26309.94 } = 162.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 162.2 }{ 11 } = 29.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 162.2 }{ 30 } = 10.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 162.2 }{ 30 } = 10.81 ; ;

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**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 21° 7'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-11**2-30**2 }{ 2 * 11 * 30 } ) = 79° 26'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-11**2-30**2 }{ 2 * 30 * 11 } ) = 79° 26'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 162.2 }{ 35.5 } = 4.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 7'41" } = 15.26 ; ;




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