22 26 27 triangle

Acute scalene triangle.

Sides: a = 22   b = 26   c = 27

Area: T = 264.9266286918
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 49.00657788267° = 49°21″ = 0.8555312193 rad
Angle ∠ B = β = 63.12766279273° = 63°7'36″ = 1.1021767503 rad
Angle ∠ C = γ = 67.8687593246° = 67°52'3″ = 1.18545129575 rad

Height: ha = 24.08442079016
Height: hb = 20.37989451475
Height: hc = 19.62441694013

Median: ma = 24.11443111036
Median: mb = 20.91765006634
Median: mc = 19.94436706752

Inradius: r = 7.06547009845
Circumradius: R = 14.57438652246

Vertex coordinates: A[27; 0] B[0; 0] C[9.94444444444; 19.62441694013]
Centroid: CG[12.31548148148; 6.54113898004]
Coordinates of the circumscribed circle: U[13.5; 5.49106782446]
Coordinates of the inscribed circle: I[11.5; 7.06547009845]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.9944221173° = 130°59'39″ = 0.8555312193 rad
∠ B' = β' = 116.8733372073° = 116°52'24″ = 1.1021767503 rad
∠ C' = γ' = 112.1322406754° = 112°7'57″ = 1.18545129575 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 = 22 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 22+26+27 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-22)(37.5-26)(37.5-27) } ; ; T = sqrt{ 70185.94 } = 264.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 264.93 }{ 22 } = 24.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 264.93 }{ 26 } = 20.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 264.93 }{ 27 } = 19.62 ; ;

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{ 22**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 49° 21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 63° 7'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-22**2-26**2 }{ 2 * 26 * 22 } ) = 67° 52'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 264.93 }{ 37.5 } = 7.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 49° 21" } = 14.57 ; ;




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