12 24 30 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 24   c = 30

Area: T = 136.7888157382
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 22.33216450092° = 22°19'54″ = 0.39897607328 rad
Angle ∠ B = β = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ C = γ = 108.2109956864° = 108°12'36″ = 1.88986200307 rad

Height: ha = 22.79880262304
Height: hb = 11.39990131152
Height: hc = 9.11992104921

Median: ma = 26.4955282599
Median: mb = 19.44222220952
Median: mc = 11.61989500386

Inradius: r = 4.14550956782
Circumradius: R = 15.7910840679

Vertex coordinates: A[30; 0] B[0; 0] C[7.8; 9.11992104921]
Centroid: CG[12.6; 3.04397368307]
Coordinates of the circumscribed circle: U[15; -4.93546377122]
Coordinates of the inscribed circle: I[9; 4.14550956782]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6688354991° = 157°40'6″ = 0.39897607328 rad
∠ B' = β' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ C' = γ' = 71.79900431357° = 71°47'24″ = 1.88986200307 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 = 24 ; ; c = 30 ; ;

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

p = a+b+c = 12+24+30 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-12)(33-24)(33-30) } ; ; T = sqrt{ 18711 } = 136.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 136.79 }{ 12 } = 22.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 136.79 }{ 24 } = 11.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 136.79 }{ 30 } = 9.12 ; ;

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**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 22° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-12**2-30**2 }{ 2 * 12 * 30 } ) = 49° 27'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-12**2-24**2 }{ 2 * 24 * 12 } ) = 108° 12'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 136.79 }{ 33 } = 4.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 22° 19'54" } = 15.79 ; ;




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

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