2348 1260.2 1377.5 triangle

Obtuse scalene triangle.

Sides: a = 2348   b = 1260.2   c = 1377.5

Area: T = 704584.0366068
Perimeter: p = 4985.7
Semiperimeter: s = 2492.85

Angle ∠ A = α = 125.7311008302° = 125°43'52″ = 2.19444200667 rad
Angle ∠ B = β = 25.82989205722° = 25°49'44″ = 0.45107997062 rad
Angle ∠ C = γ = 28.44400711259° = 28°26'24″ = 0.49663728806 rad

Height: ha = 600.1576759854
Height: hb = 1118.210986521
Height: hc = 1022.998952605

Median: ma = 603.7622490554
Median: mb = 1818.868753641
Median: mc = 1753.918774536

Inradius: r = 282.6421970463
Circumradius: R = 1446.227673285

Vertex coordinates: A[1377.5; 0] B[0; 0] C[2113.432238113; 1022.998952605]
Centroid: CG[1163.644412704; 340.9976508684]
Coordinates of the circumscribed circle: U[688.75; 1271.698989943]
Coordinates of the inscribed circle: I[1232.65; 282.6421970463]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 54.26989916981° = 54°16'8″ = 2.19444200667 rad
∠ B' = β' = 154.1711079428° = 154°10'16″ = 0.45107997062 rad
∠ C' = γ' = 151.5659928874° = 151°33'36″ = 0.49663728806 rad

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How did we calculate this triangle?

a = 2348 ; ; b = 1260.2 ; ; c = 1377.5 ; ;

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

p = a+b+c = 2348+1260.2+1377.5 = 4985.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4985.7 }{ 2 } = 2492.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2492.85 * (2492.85-2348)(2492.85-1260.2)(2492.85-1377.5) } ; ; T = sqrt{ 496438663882 } = 704584.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 704584.04 }{ 2348 } = 600.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 704584.04 }{ 1260.2 } = 1118.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 704584.04 }{ 1377.5 } = 1022.99 ; ;

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{ 2348**2-1260.2**2-1377.5**2 }{ 2 * 1260.2 * 1377.5 } ) = 125° 43'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1260.2**2-2348**2-1377.5**2 }{ 2 * 2348 * 1377.5 } ) = 25° 49'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1377.5**2-2348**2-1260.2**2 }{ 2 * 1260.2 * 2348 } ) = 28° 26'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 704584.04 }{ 2492.85 } = 282.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2348 }{ 2 * sin 125° 43'52" } = 1446.23 ; ;




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