22615 26544 19782 triangle

Acute scalene triangle.

Sides: a = 22615   b = 26544   c = 19782

Area: T = 218128887.654
Perimeter: p = 68941
Semiperimeter: s = 34470.5

Angle ∠ A = α = 56.18329995073° = 56°10'59″ = 0.9810578325 rad
Angle ∠ B = β = 77.20330508408° = 77°12'11″ = 1.34774474298 rad
Angle ∠ C = γ = 46.61439496519° = 46°36'50″ = 0.81435668988 rad

Height: ha = 19290.63878646
Height: hb = 16435.26988106
Height: hc = 22053.26994019

Median: ma = 20496.24877969
Median: mb = 16590.26549316
Median: mc = 22587.14767764

Inradius: r = 6327.987734147
Circumradius: R = 13610.05881973

Vertex coordinates: A[19782; 0] B[0; 0] C[5009.145500556; 22053.26994019]
Centroid: CG[8263.715500185; 7351.098980064]
Coordinates of the circumscribed circle: U[9891; 9348.893315015]
Coordinates of the inscribed circle: I[7926.5; 6327.987734147]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.8177000493° = 123°49'1″ = 0.9810578325 rad
∠ B' = β' = 102.7976949159° = 102°47'49″ = 1.34774474298 rad
∠ C' = γ' = 133.3866050348° = 133°23'10″ = 0.81435668988 rad

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How did we calculate this triangle?

a = 22615 ; ; b = 26544 ; ; c = 19782 ; ;

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

p = a+b+c = 22615+26544+19782 = 68941 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68941 }{ 2 } = 34470.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34470.5 * (34470.5-22615)(34470.5-26544)(34470.5-19782) } ; ; T = sqrt{ 4.758 * 10**{ 16 } } = 218128887.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 218128887.65 }{ 22615 } = 19290.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 218128887.65 }{ 26544 } = 16435.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 218128887.65 }{ 19782 } = 22053.27 ; ;

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{ 26544**2+19782**2-22615**2 }{ 2 * 26544 * 19782 } ) = 56° 10'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 22615**2+19782**2-26544**2 }{ 2 * 22615 * 19782 } ) = 77° 12'11" ; ; gamma = 180° - alpha - beta = 180° - 56° 10'59" - 77° 12'11" = 46° 36'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 218128887.65 }{ 34470.5 } = 6327.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 22615 }{ 2 * sin 56° 10'59" } = 13610.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26544**2+2 * 19782**2 - 22615**2 } }{ 2 } = 20496.248 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19782**2+2 * 22615**2 - 26544**2 } }{ 2 } = 16590.265 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26544**2+2 * 22615**2 - 19782**2 } }{ 2 } = 22587.147 ; ;
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