13 14 26 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 14   c = 26

Area: T = 47.28657007984
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 15.05988800618° = 15°3'32″ = 0.26328270387 rad
Angle ∠ B = β = 16.24880921657° = 16°14'53″ = 0.28435827055 rad
Angle ∠ C = γ = 148.6933027773° = 148°41'35″ = 2.59551829094 rad

Height: ha = 7.27547231998
Height: hb = 6.75551001141
Height: hc = 3.63773615999

Median: ma = 19.8433134833
Median: mb = 19.32661480901
Median: mc = 3.67442346142

Inradius: r = 1.78443660679
Circumradius: R = 25.01881340241

Vertex coordinates: A[26; 0] B[0; 0] C[12.48107692308; 3.63773615999]
Centroid: CG[12.82769230769; 1.21224538666]
Coordinates of the circumscribed circle: U[13; -21.37553837404]
Coordinates of the inscribed circle: I[12.5; 1.78443660679]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.9411119938° = 164°56'28″ = 0.26328270387 rad
∠ B' = β' = 163.7521907834° = 163°45'7″ = 0.28435827055 rad
∠ C' = γ' = 31.30769722275° = 31°18'25″ = 2.59551829094 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 = 14 ; ; c = 26 ; ;

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

p = a+b+c = 13+14+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-13)(26.5-14)(26.5-26) } ; ; T = sqrt{ 2235.94 } = 47.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.29 }{ 13 } = 7.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.29 }{ 14 } = 6.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.29 }{ 26 } = 3.64 ; ;

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**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 15° 3'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 16° 14'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-14**2 }{ 2 * 14 * 13 } ) = 148° 41'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.29 }{ 26.5 } = 1.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 15° 3'32" } = 25.02 ; ;




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

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