4 24 24 triangle

Acute isosceles triangle.

Sides: a = 4   b = 24   c = 24

Area: T = 47.83330429724
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 9.56603836944° = 9°33'37″ = 0.16768601732 rad
Angle ∠ B = β = 85.22198081528° = 85°13'11″ = 1.48773662402 rad
Angle ∠ C = γ = 85.22198081528° = 85°13'11″ = 1.48773662402 rad

Height: ha = 23.91765214862
Height: hb = 3.98660869144
Height: hc = 3.98660869144

Median: ma = 23.91765214862
Median: mb = 12.32988280059
Median: mc = 12.32988280059

Inradius: r = 1.8439732422
Circumradius: R = 12.04218849441

Vertex coordinates: A[24; 0] B[0; 0] C[0.33333333333; 3.98660869144]
Centroid: CG[8.11111111111; 1.32986956381]
Coordinates of the circumscribed circle: U[12; 1.0033490412]
Coordinates of the inscribed circle: I[2; 1.8439732422]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.4439616306° = 170°26'23″ = 0.16768601732 rad
∠ B' = β' = 94.78801918472° = 94°46'49″ = 1.48773662402 rad
∠ C' = γ' = 94.78801918472° = 94°46'49″ = 1.48773662402 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 = 4 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 4+24+24 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-4)(26-24)(26-24) } ; ; T = sqrt{ 2288 } = 47.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.83 }{ 4 } = 23.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.83 }{ 24 } = 3.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.83 }{ 24 } = 3.99 ; ;

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{ 4**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 9° 33'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-4**2-24**2 }{ 2 * 4 * 24 } ) = 85° 13'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-4**2-24**2 }{ 2 * 24 * 4 } ) = 85° 13'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.83 }{ 26 } = 1.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 9° 33'37" } = 12.04 ; ;




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