38 38 53.74 triangle

Right isosceles triangle.

Sides: a = 38   b = 38   c = 53.74

Area: T = 7221.999999993
Perimeter: p = 129.74
Semiperimeter: s = 64.87

Angle ∠ A = α = 455.0001230034° = 45° = 0.78554003102 rad
Angle ∠ B = β = 455.0001230034° = 45° = 0.78554003102 rad
Angle ∠ C = γ = 909.9997539932° = 89°59'59″ = 1.57107920332 rad

Height: ha = 387.9999999996
Height: hb = 387.9999999996
Height: hc = 26.87701153701

Median: ma = 42.4855218606
Median: mb = 42.4855218606
Median: mc = 26.87701153701

Inradius: r = 11.1329952212
Circumradius: R = 26.87700000002

Vertex coordinates: A[53.74; 0] B[0; 0] C[26.87; 26.87701153701]
Centroid: CG[26.87; 8.95767051234]
Coordinates of the circumscribed circle: U[26.87; 00.0001153698]
Coordinates of the inscribed circle: I[26.87; 11.1329952212]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1354.999876997° = 135° = 0.78554003102 rad
∠ B' = β' = 1354.999876997° = 135° = 0.78554003102 rad
∠ C' = γ' = 900.0002460068° = 90°1″ = 1.57107920332 rad

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How did we calculate this triangle?

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

p = a+b+c = 38+38+53.74 = 129.74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 129.74 }{ 2 } = 64.87 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64.87 * (64.87-38)(64.87-38)(64.87-53.74) } ; ; T = sqrt{ 521284 } = 722 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 722 }{ 38 } = 38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 722 }{ 38 } = 38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 722 }{ 53.74 } = 26.87 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 38**2+53.74**2-38**2 }{ 2 * 38 * 53.74 } ) = 45° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38**2+53.74**2-38**2 }{ 2 * 38 * 53.74 } ) = 45° ; ; gamma = 180° - alpha - beta = 180° - 45° - 45° = 89° 59'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 722 }{ 64.87 } = 11.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 38 }{ 2 * sin 45° } = 26.87 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 38**2+2 * 53.74**2 - 38**2 } }{ 2 } = 42.485 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 53.74**2+2 * 38**2 - 38**2 } }{ 2 } = 42.485 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 38**2+2 * 38**2 - 53.74**2 } }{ 2 } = 26.87 ; ;
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