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: h_a = 24.94443825785
Height: h_b = 23.02655839186
Height: h_c = 19.95655060628

Median: m_a = 25.37771550809
Median: m_b = 23.85437208838
Median: m_c = 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

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.

$a = 24 ; ; b = 26 ; ; c = 30 ; ;$

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

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

6. Inradius

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

7. Circumradius

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

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