1 24 24 triangle

Acute isosceles triangle.

Sides: a = 1   b = 24   c = 24

Area: T = 11.99773955507
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 2.38774968743° = 2°23'15″ = 0.04216696813 rad
Angle ∠ B = β = 88.80662515629° = 88°48'23″ = 1.55499614861 rad
Angle ∠ C = γ = 88.80662515629° = 88°48'23″ = 1.55499614861 rad

Height: ha = 23.99547911014
Height: hb = 10.9997829626
Height: hc = 10.9997829626

Median: ma = 23.99547911014
Median: mb = 12.02108152802
Median: mc = 12.02108152802

Inradius: r = 0.49896896143
Circumradius: R = 12.00326050147

Vertex coordinates: A[24; 0] B[0; 0] C[0.02108333333; 10.9997829626]
Centroid: CG[8.00769444444; 0.33332609875]
Coordinates of the circumscribed circle: U[12; 0.25500542711]
Coordinates of the inscribed circle: I[0.5; 0.49896896143]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.6132503126° = 177°36'45″ = 0.04216696813 rad
∠ B' = β' = 91.19437484371° = 91°11'37″ = 1.55499614861 rad
∠ C' = γ' = 91.19437484371° = 91°11'37″ = 1.55499614861 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 = 1 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 1+24+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-1)(24.5-24)(24.5-24) } ; ; T = sqrt{ 143.94 } = 12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12 }{ 1 } = 23.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12 }{ 24 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12 }{ 24 } = 1 ; ;

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{ 1**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 2° 23'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-1**2-24**2 }{ 2 * 1 * 24 } ) = 88° 48'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-1**2-24**2 }{ 2 * 24 * 1 } ) = 88° 48'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12 }{ 24.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 2° 23'15" } = 12 ; ;




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