16 23 26 triangle

Acute scalene triangle.

Sides: a = 16   b = 23   c = 26

Area: T = 181.9710979829
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 37.48882410762° = 37°29'18″ = 0.65442932376 rad
Angle ∠ B = β = 61.02884677763° = 61°1'42″ = 1.06551477001 rad
Angle ∠ C = γ = 81.48332911475° = 81°29' = 1.42221517159 rad

Height: ha = 22.74663724787
Height: hb = 15.82435634634
Height: hc = 13.99877676792

Median: ma = 23.20656027717
Median: mb = 18.26988259064
Median: mc = 14.95499163877

Inradius: r = 5.59991070717
Circumradius: R = 13.14549531252

Vertex coordinates: A[26; 0] B[0; 0] C[7.75; 13.99877676792]
Centroid: CG[11.25; 4.66659225597]
Coordinates of the circumscribed circle: U[13; 1.94767389819]
Coordinates of the inscribed circle: I[9.5; 5.59991070717]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.5121758924° = 142°30'42″ = 0.65442932376 rad
∠ B' = β' = 118.9721532224° = 118°58'18″ = 1.06551477001 rad
∠ C' = γ' = 98.51767088525° = 98°31' = 1.42221517159 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 = 16 ; ; b = 23 ; ; c = 26 ; ;

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

p = a+b+c = 16+23+26 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-16)(32.5-23)(32.5-26) } ; ; T = sqrt{ 33113.44 } = 181.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 181.97 }{ 16 } = 22.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 181.97 }{ 23 } = 15.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 181.97 }{ 26 } = 14 ; ;

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{ 16**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 37° 29'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 61° 1'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-23**2 }{ 2 * 23 * 16 } ) = 81° 29' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 181.97 }{ 32.5 } = 5.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 37° 29'18" } = 13.14 ; ;




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