11 29 30 triangle

Acute scalene triangle.

Sides: a = 11   b = 29   c = 30

Area: T = 158.7455078664
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 21.40333496394° = 21°24'12″ = 0.37435589222 rad
Angle ∠ B = β = 74.17333798681° = 74°10'24″ = 1.2954569696 rad
Angle ∠ C = γ = 84.42332704925° = 84°25'24″ = 1.47334640354 rad

Height: ha = 28.86327415753
Height: hb = 10.94879364596
Height: hc = 10.58330052443

Median: ma = 28.98770660813
Median: mb = 17.32877234512
Median: mc = 16

Inradius: r = 4.53655736761
Circumradius: R = 15.07113333612

Vertex coordinates: A[30; 0] B[0; 0] C[3; 10.58330052443]
Centroid: CG[11; 3.52876684148]
Coordinates of the circumscribed circle: U[15; 1.46546123329]
Coordinates of the inscribed circle: I[6; 4.53655736761]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.5976650361° = 158°35'48″ = 0.37435589222 rad
∠ B' = β' = 105.8276620132° = 105°49'36″ = 1.2954569696 rad
∠ C' = γ' = 95.57767295075° = 95°34'36″ = 1.47334640354 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 11+29+30 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-11)(35-29)(35-30) } ; ; T = sqrt{ 25200 } = 158.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 158.75 }{ 11 } = 28.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 158.75 }{ 29 } = 10.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 158.75 }{ 30 } = 10.58 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 21° 24'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-11**2-30**2 }{ 2 * 11 * 30 } ) = 74° 10'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-11**2-29**2 }{ 2 * 29 * 11 } ) = 84° 25'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 158.75 }{ 35 } = 4.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 24'12" } = 15.07 ; ;




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