6 8 12 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 8   c = 12

Area: T = 21.33107290077
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 26.38443297494° = 26°23'4″ = 0.46604934251 rad
Angle ∠ B = β = 36.33660575146° = 36°20'10″ = 0.63441838408 rad
Angle ∠ C = γ = 117.2879612736° = 117°16'47″ = 2.04769153877 rad

Height: ha = 7.11102430026
Height: hb = 5.33326822519
Height: hc = 3.55551215013

Median: ma = 9.74767943448
Median: mb = 8.6022325267
Median: mc = 3.74216573868

Inradius: r = 1.64108253083
Circumradius: R = 6.75108241255

Vertex coordinates: A[12; 0] B[0; 0] C[4.83333333333; 3.55551215013]
Centroid: CG[5.61111111111; 1.18550405004]
Coordinates of the circumscribed circle: U[6; -3.09441277242]
Coordinates of the inscribed circle: I[5; 1.64108253083]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6165670251° = 153°36'56″ = 0.46604934251 rad
∠ B' = β' = 143.6643942485° = 143°39'50″ = 0.63441838408 rad
∠ C' = γ' = 62.7220387264° = 62°43'13″ = 2.04769153877 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 = 12 ; ;

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

p = a+b+c = 6+8+12 = 26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26 }{ 2 } = 13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13 * (13-6)(13-8)(13-12) } ; ; T = sqrt{ 455 } = 21.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.33 }{ 6 } = 7.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.33 }{ 8 } = 5.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.33 }{ 12 } = 3.56 ; ;

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**2-12**2 }{ 2 * 8 * 12 } ) = 26° 23'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-6**2-12**2 }{ 2 * 6 * 12 } ) = 36° 20'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-6**2-8**2 }{ 2 * 8 * 6 } ) = 117° 16'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.33 }{ 13 } = 1.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 26° 23'4" } = 6.75 ; ;




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

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