6 20 24 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 20   c = 24

Area: T = 48.7343971724
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 11.71658523949° = 11°42'57″ = 0.2044480199 rad
Angle ∠ B = β = 42.59988128925° = 42°35'56″ = 0.74334895424 rad
Angle ∠ C = γ = 125.6855334713° = 125°41'7″ = 2.19436229122 rad

Height: ha = 16.24546572413
Height: hb = 4.87333971724
Height: hc = 4.06111643103

Median: ma = 21.88660686282
Median: mb = 14.35327000944
Median: mc = 8.6022325267

Inradius: r = 1.9499358869
Circumradius: R = 14.774408827

Vertex coordinates: A[24; 0] B[0; 0] C[4.41766666667; 4.06111643103]
Centroid: CG[9.47222222222; 1.35437214368]
Coordinates of the circumscribed circle: U[12; -8.61882181575]
Coordinates of the inscribed circle: I[5; 1.9499358869]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2844147605° = 168°17'3″ = 0.2044480199 rad
∠ B' = β' = 137.4011187108° = 137°24'4″ = 0.74334895424 rad
∠ C' = γ' = 54.31546652873° = 54°18'53″ = 2.19436229122 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 = 20 ; ; c = 24 ; ;

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

p = a+b+c = 6+20+24 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-6)(25-20)(25-24) } ; ; T = sqrt{ 2375 } = 48.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48.73 }{ 6 } = 16.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48.73 }{ 20 } = 4.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48.73 }{ 24 } = 4.06 ; ;

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**2-20**2-24**2 }{ 2 * 20 * 24 } ) = 11° 42'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-6**2-24**2 }{ 2 * 6 * 24 } ) = 42° 35'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-6**2-20**2 }{ 2 * 20 * 6 } ) = 125° 41'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48.73 }{ 25 } = 1.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 42'57" } = 14.77 ; ;




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

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