24 26 30 triangle

Acute scalene triangle.

Sides: a = 24   b = 26   c = 30

Area: T = 299.3332590942
Perimeter: p = 80
Semiperimeter: s = 40

Angle ∠ A = α = 50.132165845° = 50°7'54″ = 0.87549624994 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 73.61773301459° = 73°37'2″ = 1.28548647976 rad

Height: ha = 24.94443825785
Height: hb = 23.02655839186
Height: hc = 19.95655060628

Median: ma = 25.37771550809
Median: mb = 23.85437208838
Median: mc = 20.02549843945

Inradius: r = 7.48333147735
Circumradius: R = 15.63547826519

Vertex coordinates: A[30; 0] B[0; 0] C[13.33333333333; 19.95655060628]
Centroid: CG[14.44444444444; 6.65218353543]
Coordinates of the circumscribed circle: U[15; 4.41098104916]
Coordinates of the inscribed circle: I[14; 7.48333147735]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.868834155° = 129°52'6″ = 0.87549624994 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 106.3832669854° = 106°22'58″ = 1.28548647976 rad

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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 = 24 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 24+26+30 = 80 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 80 }{ 2 } = 40 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40 * (40-24)(40-26)(40-30) } ; ; T = sqrt{ 89600 } = 299.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 299.33 }{ 24 } = 24.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 299.33 }{ 26 } = 23.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 299.33 }{ 30 } = 19.96 ; ;

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{ 26**2+30**2-24**2 }{ 2 * 26 * 30 } ) = 50° 7'54" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24**2+30**2-26**2 }{ 2 * 24 * 30 } ) = 56° 15'4" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 24**2+26**2-30**2 }{ 2 * 24 * 26 } ) = 73° 37'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 299.33 }{ 40 } = 7.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 50° 7'54" } = 15.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 30**2 - 24**2 } }{ 2 } = 25.377 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 24**2 - 26**2 } }{ 2 } = 23.854 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 24**2 - 30**2 } }{ 2 } = 20.025 ; ;
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