18 24 24 triangle

Acute isosceles triangle.

Sides: a = 18   b = 24   c = 24

Area: T = 200.2377359152
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 67.9765687163° = 67°58'32″ = 1.18663995523 rad

Height: ha = 22.24985954613
Height: hb = 16.6866446596
Height: hc = 16.6866446596

Median: ma = 22.24985954613
Median: mb = 17.49328556845
Median: mc = 17.49328556845

Inradius: r = 6.06877987622
Circumradius: R = 12.94546373593

Vertex coordinates: A[24; 0] B[0; 0] C[6.75; 16.6866446596]
Centroid: CG[10.25; 5.56221488653]
Coordinates of the circumscribed circle: U[12; 4.85442390097]
Coordinates of the inscribed circle: I[9; 6.06877987622]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 112.0244312837° = 112°1'28″ = 1.18663995523 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 = 18 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 18+24+24 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-18)(33-24)(33-24) } ; ; T = sqrt{ 40095 } = 200.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 200.24 }{ 18 } = 22.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 200.24 }{ 24 } = 16.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 200.24 }{ 24 } = 16.69 ; ;

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{ 18**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 44° 2'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-18**2-24**2 }{ 2 * 24 * 18 } ) = 67° 58'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 200.24 }{ 33 } = 6.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 44° 2'55" } = 12.94 ; ;




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