620 500 620 triangle

Acute isosceles triangle.

Sides: a = 620   b = 500   c = 620

Area: T = 141840.5879525
Perimeter: p = 1740
Semiperimeter: s = 870

Angle ∠ A = α = 66.22200052686° = 66°13'12″ = 1.15657571226 rad
Angle ∠ B = β = 47.56599894628° = 47°33'36″ = 0.83300784083 rad
Angle ∠ C = γ = 66.22200052686° = 66°13'12″ = 1.15657571226 rad

Height: ha = 457.5550256532
Height: hb = 567.36223181
Height: hc = 457.5550256532

Median: ma = 470.213271782
Median: mb = 567.36223181
Median: mc = 470.213271782

Inradius: r = 163.0355148879
Circumradius: R = 338.7610601239

Vertex coordinates: A[620; 0] B[0; 0] C[418.3877096774; 457.5550256532]
Centroid: CG[346.1299032258; 152.5176752177]
Coordinates of the circumscribed circle: U[310; 136.5977016629]
Coordinates of the inscribed circle: I[370; 163.0355148879]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 113.7879994731° = 113°46'48″ = 1.15657571226 rad
∠ B' = β' = 132.4440010537° = 132°26'24″ = 0.83300784083 rad
∠ C' = γ' = 113.7879994731° = 113°46'48″ = 1.15657571226 rad

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How did we calculate this triangle?

a = 620 ; ; b = 500 ; ; c = 620 ; ;

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

p = a+b+c = 620+500+620 = 1740 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1740 }{ 2 } = 870 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 870 * (870-620)(870-500)(870-620) } ; ; T = sqrt{ 20118750000 } = 141840.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 141840.58 }{ 620 } = 457.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 141840.58 }{ 500 } = 567.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 141840.58 }{ 620 } = 457.55 ; ;

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{ 620**2-500**2-620**2 }{ 2 * 500 * 620 } ) = 66° 13'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 500**2-620**2-620**2 }{ 2 * 620 * 620 } ) = 47° 33'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 620**2-620**2-500**2 }{ 2 * 500 * 620 } ) = 66° 13'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 141840.58 }{ 870 } = 163.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 620 }{ 2 * sin 66° 13'12" } = 338.76 ; ;




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