18 21 24 triangle

Acute scalene triangle.

Sides: a = 18   b = 21   c = 24

Area: T = 182.9988463108
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ B = β = 57.91100487437° = 57°54'36″ = 1.01107210206 rad
Angle ∠ C = γ = 75.52224878141° = 75°31'21″ = 1.31881160717 rad

Height: ha = 20.33331625676
Height: hb = 17.42884250579
Height: hc = 15.25498719257

Median: ma = 20.67660731281
Median: mb = 18.43223085912
Median: mc = 15.44334452115

Inradius: r = 5.80994750193
Circumradius: R = 12.39435467079

Vertex coordinates: A[24; 0] B[0; 0] C[9.56325; 15.25498719257]
Centroid: CG[11.18875; 5.08332906419]
Coordinates of the circumscribed circle: U[12; 3.0988386677]
Coordinates of the inscribed circle: I[10.5; 5.80994750193]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ B' = β' = 122.0989951256° = 122°5'24″ = 1.01107210206 rad
∠ C' = γ' = 104.4787512186° = 104°28'39″ = 1.31881160717 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 = 21 ; ; c = 24 ; ;

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

p = a+b+c = 18+21+24 = 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)(31.5-21)(31.5-24) } ; ; T = sqrt{ 33488.44 } = 183 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 183 }{ 18 } = 20.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 183 }{ 21 } = 17.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 183 }{ 24 } = 15.25 ; ;

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**2-21**2-24**2 }{ 2 * 21 * 24 } ) = 46° 34'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 57° 54'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-18**2-21**2 }{ 2 * 21 * 18 } ) = 75° 31'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 183 }{ 31.5 } = 5.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 46° 34'3" } = 12.39 ; ;




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

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