55 48 73 triangle

Right scalene triangle.

Sides: a = 55   b = 48   c = 73

Area: T = 1320
Perimeter: p = 176
Semiperimeter: s = 88

Angle ∠ A = α = 48.88879095608° = 48°53'16″ = 0.85332549863 rad
Angle ∠ B = β = 41.11220904392° = 41°6'44″ = 0.71875413405 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 48
Height: hb = 55
Height: hc = 36.16443835616

Median: ma = 55.32195263899
Median: mb = 60.00883327547
Median: mc = 36.5

Inradius: r = 15
Circumradius: R = 36.5

Vertex coordinates: A[73; 0] B[0; 0] C[41.43883561644; 36.16443835616]
Centroid: CG[38.14661187215; 12.05547945205]
Coordinates of the circumscribed circle: U[36.5; 0]
Coordinates of the inscribed circle: I[40; 15]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.1122090439° = 131°6'44″ = 0.85332549863 rad
∠ B' = β' = 138.8887909561° = 138°53'16″ = 0.71875413405 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

a = 55 ; ; b = 48 ; ; c = 73 ; ;

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

p = a+b+c = 55+48+73 = 176 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 176 }{ 2 } = 88 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 88 * (88-55)(88-48)(88-73) } ; ; T = sqrt{ 1742400 } = 1320 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1320 }{ 55 } = 48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1320 }{ 48 } = 55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1320 }{ 73 } = 36.16 ; ;

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{ 55**2-48**2-73**2 }{ 2 * 48 * 73 } ) = 48° 53'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 48**2-55**2-73**2 }{ 2 * 55 * 73 } ) = 41° 6'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 73**2-55**2-48**2 }{ 2 * 48 * 55 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1320 }{ 88 } = 15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 55 }{ 2 * sin 48° 53'16" } = 36.5 ; ;




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