5 8 12 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 8   c = 12

Area: T = 14.52436875483
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 17.61224390704° = 17°36'45″ = 0.30773950511 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 133.4332536558° = 133°25'57″ = 2.32988370922 rad

Height: ha = 5.80994750193
Height: hb = 3.63109218871
Height: hc = 2.42106145914

Median: ma = 9.88768599666
Median: mb = 8.27664726786
Median: mc = 2.91554759474

Inradius: r = 1.16218950039
Circumradius: R = 8.26223644719

Vertex coordinates: A[12; 0] B[0; 0] C[4.375; 2.42106145914]
Centroid: CG[5.45883333333; 0.80768715305]
Coordinates of the circumscribed circle: U[6; -5.68803755744]
Coordinates of the inscribed circle: I[4.5; 1.16218950039]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.388756093° = 162°23'15″ = 0.30773950511 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 46.56774634422° = 46°34'3″ = 2.32988370922 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 = 5 ; ; b = 8 ; ; c = 12 ; ;

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

p = a+b+c = 5+8+12 = 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 * (12.5-5)(12.5-8)(12.5-12) } ; ; T = sqrt{ 210.94 } = 14.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.52 }{ 5 } = 5.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.52 }{ 8 } = 3.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.52 }{ 12 } = 2.42 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 8**2+12**2-5**2 }{ 2 * 8 * 12 } ) = 17° 36'45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+12**2-8**2 }{ 2 * 5 * 12 } ) = 28° 57'18" ; ; gamma = 180° - alpha - beta = 180° - 17° 36'45" - 28° 57'18" = 133° 25'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.52 }{ 12.5 } = 1.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 17° 36'45" } = 8.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 12**2 - 5**2 } }{ 2 } = 9.887 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 5**2 - 8**2 } }{ 2 } = 8.276 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 5**2 - 12**2 } }{ 2 } = 2.915 ; ;
Calculate another triangle

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

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