18 26 27 triangle

Acute scalene triangle.

Sides: a = 18   b = 26   c = 27

Area: T = 223.9787537936
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 39.65112276303° = 39°39'4″ = 0.69220444746 rad
Angle ∠ B = β = 67.17985871587° = 67°10'43″ = 1.17224875328 rad
Angle ∠ C = γ = 73.17701852111° = 73°10'13″ = 1.27770606462 rad

Height: ha = 24.8866393104
Height: hb = 17.22990413797
Height: hc = 16.5910928736

Median: ma = 24.93299017246
Median: mb = 18.90876704012
Median: mc = 17.826554347

Inradius: r = 6.30992264207
Circumradius: R = 14.10440928885

Vertex coordinates: A[27; 0] B[0; 0] C[6.98114814815; 16.5910928736]
Centroid: CG[11.32771604938; 5.53303095787]
Coordinates of the circumscribed circle: U[13.5; 4.08435568085]
Coordinates of the inscribed circle: I[9.5; 6.30992264207]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.349877237° = 140°20'56″ = 0.69220444746 rad
∠ B' = β' = 112.8211412841° = 112°49'17″ = 1.17224875328 rad
∠ C' = γ' = 106.8329814789° = 106°49'47″ = 1.27770606462 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 = 26 ; ; c = 27 ; ;

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

p = a+b+c = 18+26+27 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-18)(35.5-26)(35.5-27) } ; ; T = sqrt{ 50165.94 } = 223.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 223.98 }{ 18 } = 24.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 223.98 }{ 26 } = 17.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 223.98 }{ 27 } = 16.59 ; ;

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**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 39° 39'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-18**2-27**2 }{ 2 * 18 * 27 } ) = 67° 10'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-18**2-26**2 }{ 2 * 26 * 18 } ) = 73° 10'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 223.98 }{ 35.5 } = 6.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 39° 39'4" } = 14.1 ; ;




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