14 24 24 triangle

Acute isosceles triangle.

Sides: a = 14   b = 24   c = 24

Area: T = 160.6955363966
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 33.91655266° = 33°54'56″ = 0.59219376067 rad
Angle ∠ B = β = 73.04222367° = 73°2'32″ = 1.27548275234 rad
Angle ∠ C = γ = 73.04222367° = 73°2'32″ = 1.27548275234 rad

Height: ha = 22.95664805665
Height: hb = 13.39112803305
Height: hc = 13.39112803305

Median: ma = 22.95664805665
Median: mb = 15.55663491861
Median: mc = 15.55663491861

Inradius: r = 5.18437214182
Circumradius: R = 12.54554770458

Vertex coordinates: A[24; 0] B[0; 0] C[4.08333333333; 13.39112803305]
Centroid: CG[9.36111111111; 4.46437601102]
Coordinates of the circumscribed circle: U[12; 3.65990974717]
Coordinates of the inscribed circle: I[7; 5.18437214182]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.08444734° = 146°5'4″ = 0.59219376067 rad
∠ B' = β' = 106.95877633° = 106°57'28″ = 1.27548275234 rad
∠ C' = γ' = 106.95877633° = 106°57'28″ = 1.27548275234 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 = 14 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 14+24+24 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-14)(31-24)(31-24) } ; ; T = sqrt{ 25823 } = 160.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 160.7 }{ 14 } = 22.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 160.7 }{ 24 } = 13.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 160.7 }{ 24 } = 13.39 ; ;

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{ 14**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 33° 54'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 73° 2'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-14**2-24**2 }{ 2 * 24 * 14 } ) = 73° 2'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 160.7 }{ 31 } = 5.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 33° 54'56" } = 12.55 ; ;




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