18 22 23 triangle

Acute scalene triangle.

Sides: a = 18   b = 22   c = 23

Area: T = 185.3087683327
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 47.09114606422° = 47°5'29″ = 0.82219010378 rad
Angle ∠ B = β = 63.53549277848° = 63°32'6″ = 1.10988936799 rad
Angle ∠ C = γ = 69.3743611573° = 69°22'25″ = 1.21107979359 rad

Height: ha = 20.59897425919
Height: hb = 16.84661530297
Height: hc = 16.11437115936

Median: ma = 20.62876513447
Median: mb = 17.47985582929
Median: mc = 16.48548415218

Inradius: r = 5.88327835977
Circumradius: R = 12.28876718284

Vertex coordinates: A[23; 0] B[0; 0] C[8.02217391304; 16.11437115936]
Centroid: CG[10.34105797101; 5.37112371979]
Coordinates of the circumscribed circle: U[11.5; 4.32986116668]
Coordinates of the inscribed circle: I[9.5; 5.88327835977]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.9098539358° = 132°54'31″ = 0.82219010378 rad
∠ B' = β' = 116.4655072215° = 116°27'54″ = 1.10988936799 rad
∠ C' = γ' = 110.6266388427° = 110°37'35″ = 1.21107979359 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 = 18 ; ; b = 22 ; ; c = 23 ; ;

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

p = a+b+c = 18+22+23 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-18)(31.5-22)(31.5-23) } ; ; T = sqrt{ 34338.94 } = 185.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 185.31 }{ 18 } = 20.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 185.31 }{ 22 } = 16.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 185.31 }{ 23 } = 16.11 ; ;

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{ 18**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 47° 5'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-18**2-23**2 }{ 2 * 18 * 23 } ) = 63° 32'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-18**2-22**2 }{ 2 * 22 * 18 } ) = 69° 22'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 185.31 }{ 31.5 } = 5.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 47° 5'29" } = 12.29 ; ;




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

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