19 24 24 triangle

Acute isosceles triangle.

Sides: a = 19   b = 24   c = 24

Area: T = 209.3777499985
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 46.63659141307° = 46°38'9″ = 0.81439502513 rad
Angle ∠ B = β = 66.68220429347° = 66°40'55″ = 1.16438212012 rad
Angle ∠ C = γ = 66.68220429347° = 66°40'55″ = 1.16438212012 rad

Height: ha = 22.04397368405
Height: hb = 17.44881249988
Height: hc = 17.44881249988

Median: ma = 22.04397368405
Median: mb = 18.01438835347
Median: mc = 18.01438835347

Inradius: r = 6.25500746264
Circumradius: R = 13.067730666

Vertex coordinates: A[24; 0] B[0; 0] C[7.52108333333; 17.44881249988]
Centroid: CG[10.50769444444; 5.81660416663]
Coordinates of the circumscribed circle: U[12; 5.17224755529]
Coordinates of the inscribed circle: I[9.5; 6.25500746264]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.3644085869° = 133°21'51″ = 0.81439502513 rad
∠ B' = β' = 113.3187957065° = 113°19'5″ = 1.16438212012 rad
∠ C' = γ' = 113.3187957065° = 113°19'5″ = 1.16438212012 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 = 19 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 19+24+24 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-19)(33.5-24)(33.5-24) } ; ; T = sqrt{ 43838.94 } = 209.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 209.38 }{ 19 } = 22.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 209.38 }{ 24 } = 17.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 209.38 }{ 24 } = 17.45 ; ;

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{ 19**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 46° 38'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-19**2-24**2 }{ 2 * 19 * 24 } ) = 66° 40'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-19**2-24**2 }{ 2 * 24 * 19 } ) = 66° 40'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 209.38 }{ 33.5 } = 6.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 46° 38'9" } = 13.07 ; ;




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