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

Calculate another triangle




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" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; 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 = 180° - alpha - beta = 180° - 32° 34'42" - 57° 47'38" = 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 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.