18 19 26 triangle

Acute scalene triangle.

Sides: a = 18   b = 19   c = 26

Area: T = 170.9855196728
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 43.80883029818° = 43°48'30″ = 0.76545991267 rad
Angle ∠ B = β = 46.94656106092° = 46°56'44″ = 0.81993554745 rad
Angle ∠ C = γ = 89.2466086409° = 89°14'46″ = 1.55876380524 rad

Height: ha = 18.9988355192
Height: hb = 17.99884417608
Height: hc = 13.15327074406

Median: ma = 20.91765006634
Median: mb = 20.242228248
Median: mc = 13.17219398723

Inradius: r = 5.42881014834
Circumradius: R = 13.00111254924

Vertex coordinates: A[26; 0] B[0; 0] C[12.28884615385; 13.15327074406]
Centroid: CG[12.76328205128; 4.38442358135]
Coordinates of the circumscribed circle: U[13; 0.17110674407]
Coordinates of the inscribed circle: I[12.5; 5.42881014834]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.1921697018° = 136°11'30″ = 0.76545991267 rad
∠ B' = β' = 133.0544389391° = 133°3'16″ = 0.81993554745 rad
∠ C' = γ' = 90.7543913591° = 90°45'14″ = 1.55876380524 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 = 18 ; ; b = 19 ; ; c = 26 ; ;

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

p = a+b+c = 18+19+26 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-18)(31.5-19)(31.5-26) } ; ; T = sqrt{ 29235.94 } = 170.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 170.99 }{ 18 } = 19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 170.99 }{ 19 } = 18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 170.99 }{ 26 } = 13.15 ; ;

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{ 18**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 43° 48'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 46° 56'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-18**2-19**2 }{ 2 * 19 * 18 } ) = 89° 14'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 170.99 }{ 31.5 } = 5.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 43° 48'30" } = 13 ; ;




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