29 29 30 triangle

Acute isosceles triangle.

Sides: a = 29   b = 29   c = 30

Area: T = 372.299020938
Perimeter: p = 88
Semiperimeter: s = 44

Angle ∠ A = α = 58.85326100785° = 58°51'9″ = 1.02771718193 rad
Angle ∠ B = β = 58.85326100785° = 58°51'9″ = 1.02771718193 rad
Angle ∠ C = γ = 62.2954779843° = 62°17'41″ = 1.08772490151 rad

Height: ha = 25.67551868538
Height: hb = 25.67551868538
Height: hc = 24.8199347292

Median: ma = 25.69553303151
Median: mb = 25.69553303151
Median: mc = 24.8199347292

Inradius: r = 8.46111411223
Circumradius: R = 16.94224278186

Vertex coordinates: A[30; 0] B[0; 0] C[15; 24.8199347292]
Centroid: CG[15; 8.2733115764]
Coordinates of the circumscribed circle: U[15; 7.87769194733]
Coordinates of the inscribed circle: I[15; 8.46111411223]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.1477389922° = 121°8'51″ = 1.02771718193 rad
∠ B' = β' = 121.1477389922° = 121°8'51″ = 1.02771718193 rad
∠ C' = γ' = 117.7055220157° = 117°42'19″ = 1.08772490151 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 29+29+30 = 88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 88 }{ 2 } = 44 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 44 * (44-29)(44-29)(44-30) } ; ; T = sqrt{ 138600 } = 372.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 372.29 }{ 29 } = 25.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 372.29 }{ 29 } = 25.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 372.29 }{ 30 } = 24.82 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 58° 51'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 58° 51'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 62° 17'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 372.29 }{ 44 } = 8.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 29 }{ 2 * sin 58° 51'9" } = 16.94 ; ;




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