3 6 8 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 6   c = 8

Area: T = 7.64444424257
Perimeter: p = 17
Semiperimeter: s = 8.5

Angle ∠ A = α = 18.57333497187° = 18°34'24″ = 0.32441661057 rad
Angle ∠ B = β = 39.57112194572° = 39°34'16″ = 0.69106480686 rad
Angle ∠ C = γ = 121.8555430824° = 121°51'20″ = 2.12767784793 rad

Height: ha = 5.09662949505
Height: hb = 2.54881474752
Height: hc = 1.91111106064

Median: ma = 6.91101374805
Median: mb = 5.24440442409
Median: mc = 2.55495097568

Inradius: r = 0.89993461677
Circumradius: R = 4.70993035692

Vertex coordinates: A[8; 0] B[0; 0] C[2.31325; 1.91111106064]
Centroid: CG[3.43875; 0.63770368688]
Coordinates of the circumscribed circle: U[4; -2.48554657726]
Coordinates of the inscribed circle: I[2.5; 0.89993461677]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.4276650281° = 161°25'36″ = 0.32441661057 rad
∠ B' = β' = 140.4298780543° = 140°25'44″ = 0.69106480686 rad
∠ C' = γ' = 58.1454569176° = 58°8'40″ = 2.12767784793 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 = 3 ; ; b = 6 ; ; c = 8 ; ;

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

p = a+b+c = 3+6+8 = 17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17 }{ 2 } = 8.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.5 * (8.5-3)(8.5-6)(8.5-8) } ; ; T = sqrt{ 58.44 } = 7.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.64 }{ 3 } = 5.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.64 }{ 6 } = 2.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.64 }{ 8 } = 1.91 ; ;

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{ 3**2-6**2-8**2 }{ 2 * 6 * 8 } ) = 18° 34'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6**2-3**2-8**2 }{ 2 * 3 * 8 } ) = 39° 34'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-3**2-6**2 }{ 2 * 6 * 3 } ) = 121° 51'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.64 }{ 8.5 } = 0.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 18° 34'24" } = 4.71 ; ;




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

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