5 9 13 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 9   c = 13

Area: T = 16.06882139642
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 15.94223686056° = 15°56'33″ = 0.27882468227 rad
Angle ∠ B = β = 29.63106273936° = 29°37'50″ = 0.51771520074 rad
Angle ∠ C = γ = 134.4277004001° = 134°25'37″ = 2.34661938234 rad

Height: ha = 6.42772855857
Height: hb = 3.57107142143
Height: hc = 2.47220329176

Median: ma = 10.89772473589
Median: mb = 8.7610707734
Median: mc = 3.27987192622

Inradius: r = 1.19902380714
Circumradius: R = 9.10218205462

Vertex coordinates: A[13; 0] B[0; 0] C[4.34661538462; 2.47220329176]
Centroid: CG[5.78220512821; 0.82440109725]
Coordinates of the circumscribed circle: U[6.5; -6.37112743823]
Coordinates of the inscribed circle: I[4.5; 1.19902380714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.0587631394° = 164°3'27″ = 0.27882468227 rad
∠ B' = β' = 150.3699372606° = 150°22'10″ = 0.51771520074 rad
∠ C' = γ' = 45.57329959992° = 45°34'23″ = 2.34661938234 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 = 5 ; ; b = 9 ; ; c = 13 ; ;

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

p = a+b+c = 5+9+13 = 27 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27 }{ 2 } = 13.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.5 * (13.5-5)(13.5-9)(13.5-13) } ; ; T = sqrt{ 258.19 } = 16.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.07 }{ 5 } = 6.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.07 }{ 9 } = 3.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.07 }{ 13 } = 2.47 ; ;

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{ 5**2-9**2-13**2 }{ 2 * 9 * 13 } ) = 15° 56'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-5**2-13**2 }{ 2 * 5 * 13 } ) = 29° 37'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-5**2-9**2 }{ 2 * 9 * 5 } ) = 134° 25'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.07 }{ 13.5 } = 1.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 15° 56'33" } = 9.1 ; ;




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

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