14 22 26 triangle

Acute scalene triangle.

Sides: a = 14   b = 22   c = 26

Area: T = 153.9976753213
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 32.57881984923° = 32°34'42″ = 0.56985968281 rad
Angle ∠ B = β = 57.79438546387° = 57°47'38″ = 1.00986930509 rad
Angle ∠ C = γ = 89.6287946869° = 89°37'41″ = 1.56443027747 rad

Height: ha = 221.9995361732
Height: hb = 143.9997048375
Height: hc = 11.84659040933

Median: ma = 23.04334372436
Median: mb = 17.74882393493
Median: mc = 13.07766968306

Inradius: r = 4.96876372004
Circumradius: R = 133.0002740852

Vertex coordinates: A[26; 0] B[0; 0] C[7.46215384615; 11.84659040933]
Centroid: CG[11.15438461538; 3.94986346978]
Coordinates of the circumscribed circle: U[13; 0.08444173642]
Coordinates of the inscribed circle: I[9; 4.96876372004]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.4221801508° = 147°25'18″ = 0.56985968281 rad
∠ B' = β' = 122.2066145361° = 122°12'22″ = 1.00986930509 rad
∠ C' = γ' = 90.3722053131° = 90°22'19″ = 1.56443027747 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 = 14 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 14+22+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 * (31-14)(31-22)(31-26) } ; ; T = sqrt{ 23715 } = 154 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 154 }{ 14 } = 22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 154 }{ 22 } = 14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 154 }{ 26 } = 11.85 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 22**2+26**2-14**2 }{ 2 * 22 * 26 } ) = 32° 34'42" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+26**2-22**2 }{ 2 * 14 * 26 } ) = 57° 47'38" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 14**2+22**2-26**2 }{ 2 * 14 * 22 } ) = 89° 37'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 154 }{ 31 } = 4.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 32° 34'42" } = 13 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 26**2 - 14**2 } }{ 2 } = 23.043 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 14**2 - 22**2 } }{ 2 } = 17.748 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 14**2 - 26**2 } }{ 2 } = 13.077 ; ;
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