13 23 26 triangle

Acute scalene triangle.

Sides: a = 13   b = 23   c = 26

Area: T = 149.3998795176
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 29.97876090229° = 29°58'39″ = 0.52332079793 rad
Angle ∠ B = β = 62.1310738238° = 62°7'51″ = 1.08443859489 rad
Angle ∠ C = γ = 87.89216527391° = 87°53'30″ = 1.53439987253 rad

Height: ha = 22.98444300271
Height: hb = 12.99111995805
Height: hc = 11.49222150135

Median: ma = 23.67696007571
Median: mb = 17.03767250374
Median: mc = 13.4166407865

Inradius: r = 4.81993159734
Circumradius: R = 13.0098806381

Vertex coordinates: A[26; 0] B[0; 0] C[6.07769230769; 11.49222150135]
Centroid: CG[10.69223076923; 3.83107383378]
Coordinates of the circumscribed circle: U[13; 0.47985848501]
Coordinates of the inscribed circle: I[8; 4.81993159734]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0222390977° = 150°1'21″ = 0.52332079793 rad
∠ B' = β' = 117.8699261762° = 117°52'9″ = 1.08443859489 rad
∠ C' = γ' = 92.10883472609° = 92°6'30″ = 1.53439987253 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 = 13 ; ; b = 23 ; ; c = 26 ; ;

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

p = a+b+c = 13+23+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 * (31-13)(31-23)(31-26) } ; ; T = sqrt{ 22320 } = 149.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 149.4 }{ 13 } = 22.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 149.4 }{ 23 } = 12.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 149.4 }{ 26 } = 11.49 ; ;

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{ 13**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 29° 58'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 62° 7'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-23**2 }{ 2 * 23 * 13 } ) = 87° 53'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 149.4 }{ 31 } = 4.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 29° 58'39" } = 13.01 ; ;




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

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