12 24 26 triangle

Acute scalene triangle.

Sides: a = 12   b = 24   c = 26

Area: T = 143.5799246411
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 27.39993615864° = 27°23'58″ = 0.47882090726 rad
Angle ∠ B = β = 66.98216671563° = 66°58'54″ = 1.16990506304 rad
Angle ∠ C = γ = 85.61989712574° = 85°37'8″ = 1.49443329506 rad

Height: ha = 23.93298744019
Height: hb = 11.96549372009
Height: hc = 11.04545574162

Median: ma = 24.2989915603
Median: mb = 16.31095064303
Median: mc = 13.82202749611

Inradius: r = 4.63215885939
Circumradius: R = 13.03880960117

Vertex coordinates: A[26; 0] B[0; 0] C[4.69223076923; 11.04545574162]
Centroid: CG[10.23107692308; 3.68215191387]
Coordinates of the circumscribed circle: U[13; 0.99659656676]
Coordinates of the inscribed circle: I[7; 4.63215885939]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.6010638414° = 152°36'2″ = 0.47882090726 rad
∠ B' = β' = 113.0188332844° = 113°1'6″ = 1.16990506304 rad
∠ C' = γ' = 94.38110287426° = 94°22'52″ = 1.49443329506 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 = 12 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 12+24+26 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-12)(31-24)(31-26) } ; ; T = sqrt{ 20615 } = 143.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 143.58 }{ 12 } = 23.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 143.58 }{ 24 } = 11.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 143.58 }{ 26 } = 11.04 ; ;

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{ 12**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 27° 23'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 66° 58'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-24**2 }{ 2 * 24 * 12 } ) = 85° 37'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 143.58 }{ 31 } = 4.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 27° 23'58" } = 13.04 ; ;




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