12 20 24 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 20   c = 24

Area: T = 119.7333036377
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 93.82325537293° = 93°49'21″ = 1.63875124752 rad

Height: ha = 19.95655060628
Height: hb = 11.97333036377
Height: hc = 9.97877530314

Median: ma = 21.26602916255
Median: mb = 16.12545154966
Median: mc = 11.3143708499

Inradius: r = 4.27661798706
Circumradius: R = 12.02767558861

Vertex coordinates: A[24; 0] B[0; 0] C[6.66766666667; 9.97877530314]
Centroid: CG[10.22222222222; 3.32659176771]
Coordinates of the circumscribed circle: U[12; -0.80217837257]
Coordinates of the inscribed circle: I[8; 4.27661798706]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 86.17774462707° = 86°10'39″ = 1.63875124752 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 = 12 ; ; b = 20 ; ; c = 24 ; ;

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

p = a+b+c = 12+20+24 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-12)(28-20)(28-24) } ; ; T = sqrt{ 14336 } = 119.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.73 }{ 12 } = 19.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.73 }{ 20 } = 11.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.73 }{ 24 } = 9.98 ; ;

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{ 12**2-20**2-24**2 }{ 2 * 20 * 24 } ) = 29° 55'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-12**2-24**2 }{ 2 * 12 * 24 } ) = 56° 15'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-12**2-20**2 }{ 2 * 20 * 12 } ) = 93° 49'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.73 }{ 28 } = 4.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 29° 55'35" } = 12.03 ; ;




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

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