2 23 24 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 23   c = 24

Area: T = 20.33331625676
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 4.225485799° = 4°13'29″ = 0.07437376824 rad
Angle ∠ B = β = 57.91100487437° = 57°54'36″ = 1.01107210206 rad
Angle ∠ C = γ = 117.8655093266° = 117°51'54″ = 2.05771339507 rad

Height: ha = 20.33331625676
Height: hb = 1.76881010928
Height: hc = 1.6944430214

Median: ma = 23.48440371316
Median: mb = 12.56598566871
Median: mc = 11.06879718106

Inradius: r = 0.83299250028
Circumradius: R = 13.57438844896

Vertex coordinates: A[24; 0] B[0; 0] C[1.06325; 1.6944430214]
Centroid: CG[8.35441666667; 0.56548100713]
Coordinates of the circumscribed circle: U[12; -6.34443155766]
Coordinates of the inscribed circle: I[1.5; 0.83299250028]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.775514201° = 175°46'31″ = 0.07437376824 rad
∠ B' = β' = 122.0989951256° = 122°5'24″ = 1.01107210206 rad
∠ C' = γ' = 62.13549067337° = 62°8'6″ = 2.05771339507 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 = 2 ; ; b = 23 ; ; c = 24 ; ;

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

p = a+b+c = 2+23+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-2)(24.5-23)(24.5-24) } ; ; T = sqrt{ 413.44 } = 20.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.33 }{ 2 } = 20.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.33 }{ 23 } = 1.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.33 }{ 24 } = 1.69 ; ;

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{ 2**2-23**2-24**2 }{ 2 * 23 * 24 } ) = 4° 13'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-2**2-24**2 }{ 2 * 2 * 24 } ) = 57° 54'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-2**2-23**2 }{ 2 * 23 * 2 } ) = 117° 51'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.33 }{ 24.5 } = 0.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 13'29" } = 13.57 ; ;




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

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