3 23 24 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 23   c = 24

Area: T = 33.16662479036
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 6.90217733189° = 6°54'6″ = 0.12204586686 rad
Angle ∠ B = β = 67.11546195238° = 67°6'53″ = 1.17113710869 rad
Angle ∠ C = γ = 105.9843607157° = 105°59'1″ = 1.8549762898 rad

Height: ha = 22.11108319357
Height: hb = 2.88440215568
Height: hc = 2.7643853992

Median: ma = 23.45774082115
Median: mb = 12.65989889012
Median: mc = 11.18803398875

Inradius: r = 1.32766499161
Circumradius: R = 12.48325696655

Vertex coordinates: A[24; 0] B[0; 0] C[1.16766666667; 2.7643853992]
Centroid: CG[8.38988888889; 0.9211284664]
Coordinates of the circumscribed circle: U[12; -3.43772293282]
Coordinates of the inscribed circle: I[2; 1.32766499161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.0988226681° = 173°5'54″ = 0.12204586686 rad
∠ B' = β' = 112.8855380476° = 112°53'7″ = 1.17113710869 rad
∠ C' = γ' = 74.01663928427° = 74°59″ = 1.8549762898 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 = 3 ; ; b = 23 ; ; c = 24 ; ;

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

p = a+b+c = 3+23+24 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-3)(25-23)(25-24) } ; ; T = sqrt{ 1100 } = 33.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.17 }{ 3 } = 22.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.17 }{ 23 } = 2.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.17 }{ 24 } = 2.76 ; ;

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{ 3**2-23**2-24**2 }{ 2 * 23 * 24 } ) = 6° 54'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-3**2-24**2 }{ 2 * 3 * 24 } ) = 67° 6'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-3**2-23**2 }{ 2 * 23 * 3 } ) = 105° 59'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.17 }{ 25 } = 1.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 54'6" } = 12.48 ; ;




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