3473 4822 5009.12 triangle

Acute scalene triangle.

Sides: a = 3473   b = 4822   c = 5009.12

Area: T = 7973903.164374
Perimeter: p = 13304.12
Semiperimeter: s = 6652.06

Angle ∠ A = α = 41.31993944448° = 41°19'10″ = 0.7211159478 rad
Angle ∠ B = β = 66.45105857789° = 66°27'2″ = 1.16597815117 rad
Angle ∠ C = γ = 72.23300197763° = 72°13'48″ = 1.26106516639 rad

Height: ha = 4591.943962784
Height: hb = 3307.301118778
Height: hc = 3183.754409802

Median: ma = 4599.57107775
Median: mb = 3572.616600052
Median: mc = 3374.001143841

Inradius: r = 1198.712185223
Circumradius: R = 2630.041074505

Vertex coordinates: A[5009.12; 0] B[0; 0] C[1387.60218317; 3183.754409802]
Centroid: CG[2132.241061057; 1061.251136601]
Coordinates of the circumscribed circle: U[2504.56; 802.6798968828]
Coordinates of the inscribed circle: I[1830.06; 1198.712185223]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.6810605555° = 138°40'50″ = 0.7211159478 rad
∠ B' = β' = 113.5499414221° = 113°32'58″ = 1.16597815117 rad
∠ C' = γ' = 107.7769980224° = 107°46'12″ = 1.26106516639 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 = 3473 ; ; b = 4822 ; ; c = 5009.12 ; ;

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

p = a+b+c = 3473+4822+5009.12 = 13304.12 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13304.12 }{ 2 } = 6652.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6652.06 * (6652.06-3473)(6652.06-4822)(6652.06-5009.12) } ; ; T = sqrt{ 6.358 * 10**{ 13 } } = 7973903.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7973903.16 }{ 3473 } = 4591.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7973903.16 }{ 4822 } = 3307.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7973903.16 }{ 5009.12 } = 3183.75 ; ;

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{ 4822**2+5009.12**2-3473**2 }{ 2 * 4822 * 5009.12 } ) = 41° 19'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3473**2+5009.12**2-4822**2 }{ 2 * 3473 * 5009.12 } ) = 66° 27'2" ; ;
 gamma = 180° - alpha - beta = 180° - 41° 19'10" - 66° 27'2" = 72° 13'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7973903.16 }{ 6652.06 } = 1198.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3473 }{ 2 * sin 41° 19'10" } = 2630.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4822**2+2 * 5009.12**2 - 3473**2 } }{ 2 } = 4599.571 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5009.12**2+2 * 3473**2 - 4822**2 } }{ 2 } = 3572.616 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4822**2+2 * 3473**2 - 5009.12**2 } }{ 2 } = 3374.001 ; ;
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