10 24 24 triangle

Acute isosceles triangle.

Sides: a = 10   b = 24   c = 24

Area: T = 117.3676945943
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 24.04993983611° = 24°2'58″ = 0.42197411845 rad
Angle ∠ B = β = 77.97553008194° = 77°58'31″ = 1.36109257345 rad
Angle ∠ C = γ = 77.97553008194° = 77°58'31″ = 1.36109257345 rad

Height: ha = 23.47333891886
Height: hb = 9.78105788286
Height: hc = 9.78105788286

Median: ma = 23.47333891886
Median: mb = 13.92883882772
Median: mc = 13.92883882772

Inradius: r = 4.0477136067
Circumradius: R = 12.26992124979

Vertex coordinates: A[24; 0] B[0; 0] C[2.08333333333; 9.78105788286]
Centroid: CG[8.69444444444; 3.26601929429]
Coordinates of the circumscribed circle: U[12; 2.55660859371]
Coordinates of the inscribed circle: I[5; 4.0477136067]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.9510601639° = 155°57'2″ = 0.42197411845 rad
∠ B' = β' = 102.0254699181° = 102°1'29″ = 1.36109257345 rad
∠ C' = γ' = 102.0254699181° = 102°1'29″ = 1.36109257345 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 = 10 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 10+24+24 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-10)(29-24)(29-24) } ; ; T = sqrt{ 13775 } = 117.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117.37 }{ 10 } = 23.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117.37 }{ 24 } = 9.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117.37 }{ 24 } = 9.78 ; ;

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{ 10**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 24° 2'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-10**2-24**2 }{ 2 * 10 * 24 } ) = 77° 58'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-10**2-24**2 }{ 2 * 24 * 10 } ) = 77° 58'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117.37 }{ 29 } = 4.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 24° 2'58" } = 12.27 ; ;




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