8 11 13 triangle

Acute scalene triangle.

Sides: a = 8   b = 11   c = 13

Area: T = 43.81878046004
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 37.79548789633° = 37°47'42″ = 0.66596450783 rad
Angle ∠ B = β = 57.42110296072° = 57°25'16″ = 1.00221860265 rad
Angle ∠ C = γ = 84.78440914295° = 84°47'3″ = 1.48797615488 rad

Height: ha = 10.95444511501
Height: hb = 7.96768735637
Height: hc = 6.74112007078

Median: ma = 11.35878166916
Median: mb = 9.28770878105
Median: mc = 7.08987234394

Inradius: r = 2.73986127875
Circumradius: R = 6.52770271436

Vertex coordinates: A[13; 0] B[0; 0] C[4.30876923077; 6.74112007078]
Centroid: CG[5.76992307692; 2.24770669026]
Coordinates of the circumscribed circle: U[6.5; 0.5933366104]
Coordinates of the inscribed circle: I[5; 2.73986127875]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.2055121037° = 142°12'18″ = 0.66596450783 rad
∠ B' = β' = 122.5798970393° = 122°34'44″ = 1.00221860265 rad
∠ C' = γ' = 95.21659085705° = 95°12'57″ = 1.48797615488 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 = 8 ; ; b = 11 ; ; c = 13 ; ;

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

p = a+b+c = 8+11+13 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-8)(16-11)(16-13) } ; ; T = sqrt{ 1920 } = 43.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.82 }{ 8 } = 10.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.82 }{ 11 } = 7.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.82 }{ 13 } = 6.74 ; ;

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{ 8**2-11**2-13**2 }{ 2 * 11 * 13 } ) = 37° 47'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-8**2-13**2 }{ 2 * 8 * 13 } ) = 57° 25'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-8**2-11**2 }{ 2 * 11 * 8 } ) = 84° 47'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.82 }{ 16 } = 2.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 37° 47'42" } = 6.53 ; ;




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

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