12 26 28 triangle

Acute scalene triangle.

Sides: a = 12   b = 26   c = 28

Area: T = 155.7440168229
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 25.33216750167° = 25°19'54″ = 0.44221211341 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 86.69326378203° = 86°41'34″ = 1.51330719672 rad

Height: ha = 25.95766947048
Height: hb = 11.98800129407
Height: hc = 11.12442977306

Median: ma = 26.34438797446
Median: mb = 17.17655640373
Median: mc = 14.62987388383

Inradius: r = 4.71993990372
Circumradius: R = 14.02333571392

Vertex coordinates: A[28; 0] B[0; 0] C[4.5; 11.12442977306]
Centroid: CG[10.83333333333; 3.70880992435]
Coordinates of the circumscribed circle: U[14; 0.8099039835]
Coordinates of the inscribed circle: I[7; 4.71993990372]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.6688324983° = 154°40'6″ = 0.44221211341 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 93.30773621797° = 93°18'26″ = 1.51330719672 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 = 12 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 12+26+28 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-12)(33-26)(33-28) } ; ; T = sqrt{ 24255 } = 155.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 155.74 }{ 12 } = 25.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 155.74 }{ 26 } = 11.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 155.74 }{ 28 } = 11.12 ; ;

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**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 25° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-12**2-28**2 }{ 2 * 12 * 28 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-12**2-26**2 }{ 2 * 26 * 12 } ) = 86° 41'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 155.74 }{ 33 } = 4.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 25° 19'54" } = 14.02 ; ;




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

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