29 30 30 triangle

Acute isosceles triangle.

Sides: a = 29   b = 30   c = 30

Area: T = 380.8154833613
Perimeter: p = 89
Semiperimeter: s = 44.5

Angle ∠ A = α = 57.80766690797° = 57°48'24″ = 1.00989167051 rad
Angle ∠ B = β = 61.09766654602° = 61°5'48″ = 1.06663379743 rad
Angle ∠ C = γ = 61.09766654602° = 61°5'48″ = 1.06663379743 rad

Height: ha = 26.26330919733
Height: hb = 25.38876555742
Height: hc = 25.38876555742

Median: ma = 26.26330919733
Median: mb = 25.40766920318
Median: mc = 25.40766920318

Inradius: r = 8.55876367104
Circumradius: R = 17.13443115448

Vertex coordinates: A[30; 0] B[0; 0] C[14.01766666667; 25.38876555742]
Centroid: CG[14.67222222222; 8.46325518581]
Coordinates of the circumscribed circle: U[15; 8.28215839133]
Coordinates of the inscribed circle: I[14.5; 8.55876367104]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.193333092° = 122°11'36″ = 1.00989167051 rad
∠ B' = β' = 118.903333454° = 118°54'12″ = 1.06663379743 rad
∠ C' = γ' = 118.903333454° = 118°54'12″ = 1.06663379743 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 = 29 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 29+30+30 = 89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 89 }{ 2 } = 44.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 44.5 * (44.5-29)(44.5-30)(44.5-30) } ; ; T = sqrt{ 145019.94 } = 380.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 380.81 }{ 29 } = 26.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 380.81 }{ 30 } = 25.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 380.81 }{ 30 } = 25.39 ; ;

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{ 29**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 57° 48'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 61° 5'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-29**2-30**2 }{ 2 * 30 * 29 } ) = 61° 5'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 380.81 }{ 44.5 } = 8.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 29 }{ 2 * sin 57° 48'24" } = 17.13 ; ;




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