8 13 18 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 13   c = 18

Area: T = 46.75993573523
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 23.55664643091° = 23°33'23″ = 0.41111378623 rad
Angle ∠ B = β = 40.49990559185° = 40°29'57″ = 0.70768418697 rad
Angle ∠ C = γ = 115.9444479772° = 115°56'40″ = 2.02436129215 rad

Height: ha = 11.69898393381
Height: hb = 7.1943747285
Height: hc = 5.19554841503

Median: ma = 15.18222264507
Median: mb = 12.31986849948
Median: mc = 5.95881876439

Inradius: r = 2.39879157617
Circumradius: R = 10.00986918747

Vertex coordinates: A[18; 0] B[0; 0] C[6.08333333333; 5.19554841503]
Centroid: CG[8.02877777778; 1.73218280501]
Coordinates of the circumscribed circle: U[9; -4.37988026952]
Coordinates of the inscribed circle: I[6.5; 2.39879157617]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4443535691° = 156°26'37″ = 0.41111378623 rad
∠ B' = β' = 139.5010944081° = 139°30'3″ = 0.70768418697 rad
∠ C' = γ' = 64.05655202276° = 64°3'20″ = 2.02436129215 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 = 13 ; ; c = 18 ; ;

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

p = a+b+c = 8+13+18 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-8)(19.5-13)(19.5-18) } ; ; T = sqrt{ 2186.44 } = 46.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.76 }{ 8 } = 11.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.76 }{ 13 } = 7.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.76 }{ 18 } = 5.2 ; ;

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**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 23° 33'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-8**2-18**2 }{ 2 * 8 * 18 } ) = 40° 29'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-8**2-13**2 }{ 2 * 13 * 8 } ) = 115° 56'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.76 }{ 19.5 } = 2.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 23° 33'23" } = 10.01 ; ;




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

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