19 24 26 triangle

Acute scalene triangle.

Sides: a = 19   b = 24   c = 26

Area: T = 218.4643812793
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 44.44334156294° = 44°26'36″ = 0.77656839336 rad
Angle ∠ B = β = 62.18662319147° = 62°11'10″ = 1.08553544963 rad
Angle ∠ C = γ = 73.37703524559° = 73°22'13″ = 1.28105542237 rad

Height: ha = 22.99661908203
Height: hb = 18.20553177327
Height: hc = 16.80549086764

Median: ma = 23.14662739982
Median: mb = 19.35220024804
Median: mc = 17.30660682999

Inradius: r = 6.33222844288
Circumradius: R = 13.56774643874

Vertex coordinates: A[26; 0] B[0; 0] C[8.86553846154; 16.80549086764]
Centroid: CG[11.62217948718; 5.60216362255]
Coordinates of the circumscribed circle: U[13; 3.88327940845]
Coordinates of the inscribed circle: I[10.5; 6.33222844288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5576584371° = 135°33'24″ = 0.77656839336 rad
∠ B' = β' = 117.8143768085° = 117°48'50″ = 1.08553544963 rad
∠ C' = γ' = 106.6329647544° = 106°37'47″ = 1.28105542237 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 = 19 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 19+24+26 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-19)(34.5-24)(34.5-26) } ; ; T = sqrt{ 47726.44 } = 218.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 218.46 }{ 19 } = 23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 218.46 }{ 24 } = 18.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 218.46 }{ 26 } = 16.8 ; ;

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{ 19**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 44° 26'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 62° 11'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-19**2-24**2 }{ 2 * 24 * 19 } ) = 73° 22'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 218.46 }{ 34.5 } = 6.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 44° 26'36" } = 13.57 ; ;




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