Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 19   b = 22   c = 24

Area: T = 197.8854909733
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 48.55326288331° = 48°33'9″ = 0.84774032336 rad
Angle ∠ B = β = 60.21773922406° = 60°13'3″ = 1.05109917616 rad
Angle ∠ C = γ = 71.23299789263° = 71°13'48″ = 1.24331976584 rad

Height: ha = 20.83299904982
Height: hb = 17.99895372484
Height: hc = 16.49904091444

Median: ma = 20.97702169755
Median: mb = 18.64113518823
Median: mc = 16.68883192683

Inradius: r = 6.08987664533
Circumradius: R = 12.67440336258

Vertex coordinates: A[24; 0] B[0; 0] C[9.43875; 16.49904091444]
Centroid: CG[11.14658333333; 5.49768030481]
Coordinates of the circumscribed circle: U[12; 4.07881280447]
Coordinates of the inscribed circle: I[10.5; 6.08987664533]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.4477371167° = 131°26'51″ = 0.84774032336 rad
∠ B' = β' = 119.7832607759° = 119°46'57″ = 1.05109917616 rad
∠ C' = γ' = 108.7770021074° = 108°46'12″ = 1.24331976584 rad

Calculate another triangle




How did we calculate this triangle?

a = 19 ; ; b = 22 ; ; c = 24 ; ;

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

p = a+b+c = 19+22+24 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-19)(32.5-22)(32.5-24) } ; ; T = sqrt{ 39158.44 } = 197.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197.88 }{ 19 } = 20.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197.88 }{ 22 } = 17.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197.88 }{ 24 } = 16.49 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 22**2+24**2-19**2 }{ 2 * 22 * 24 } ) = 48° 33'9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 19**2+24**2-22**2 }{ 2 * 19 * 24 } ) = 60° 13'3" ; ; gamma = 180° - alpha - beta = 180° - 48° 33'9" - 60° 13'3" = 71° 13'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197.88 }{ 32.5 } = 6.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 19 }{ 2 * sin 48° 33'9" } = 12.67 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 24**2 - 19**2 } }{ 2 } = 20.97 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 19**2 - 22**2 } }{ 2 } = 18.641 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 19**2 - 24**2 } }{ 2 } = 16.688 ; ;
Calculate another triangle

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

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