6 8 11 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 8   c = 11

Area: T = 23.4198742494
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 32.15772086093° = 32°9'26″ = 0.56112491685 rad
Angle ∠ B = β = 45.20771662976° = 45°12'26″ = 0.78990138974 rad
Angle ∠ C = γ = 102.6365625093° = 102°38'8″ = 1.79113295877 rad

Height: ha = 7.8066247498
Height: hb = 5.85546856235
Height: hc = 4.25879531807

Median: ma = 9.13878334412
Median: mb = 7.90656941504
Median: mc = 4.44440972087

Inradius: r = 1.87334993995
Circumradius: R = 5.63765110139

Vertex coordinates: A[11; 0] B[0; 0] C[4.22772727273; 4.25879531807]
Centroid: CG[5.07657575758; 1.41993177269]
Coordinates of the circumscribed circle: U[5.5; -1.23329867843]
Coordinates of the inscribed circle: I[4.5; 1.87334993995]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.8432791391° = 147°50'34″ = 0.56112491685 rad
∠ B' = β' = 134.7932833702° = 134°47'34″ = 0.78990138974 rad
∠ C' = γ' = 77.3644374907° = 77°21'52″ = 1.79113295877 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 = 6 ; ; b = 8 ; ; c = 11 ; ;

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

p = a+b+c = 6+8+11 = 25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25 }{ 2 } = 12.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.5 * (12.5-6)(12.5-8)(12.5-11) } ; ; T = sqrt{ 548.44 } = 23.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.42 }{ 6 } = 7.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.42 }{ 8 } = 5.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.42 }{ 11 } = 4.26 ; ;

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{ 6**2-8**2-11**2 }{ 2 * 8 * 11 } ) = 32° 9'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-6**2-11**2 }{ 2 * 6 * 11 } ) = 45° 12'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-6**2-8**2 }{ 2 * 8 * 6 } ) = 102° 38'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.42 }{ 12.5 } = 1.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 32° 9'26" } = 5.64 ; ;




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

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