24 29 29 triangle

Acute isosceles triangle.

Sides: a = 24   b = 29   c = 29

Area: T = 316.8099090779
Perimeter: p = 82
Semiperimeter: s = 41

Angle ∠ A = α = 48.88766708554° = 48°53'12″ = 0.85332333668 rad
Angle ∠ B = β = 65.55766645723° = 65°33'24″ = 1.14441796434 rad
Angle ∠ C = γ = 65.55766645723° = 65°33'24″ = 1.14441796434 rad

Height: ha = 26.40107575649
Height: hb = 21.84989028123
Height: hc = 21.84989028123

Median: ma = 26.40107575649
Median: mb = 22.32215142855
Median: mc = 22.32215142855

Inradius: r = 7.72770509946
Circumradius: R = 15.92875732511

Vertex coordinates: A[29; 0] B[0; 0] C[9.93110344828; 21.84989028123]
Centroid: CG[12.97770114943; 7.28329676041]
Coordinates of the circumscribed circle: U[14.5; 6.5910719966]
Coordinates of the inscribed circle: I[12; 7.72770509946]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.1133329145° = 131°6'48″ = 0.85332333668 rad
∠ B' = β' = 114.4433335428° = 114°26'36″ = 1.14441796434 rad
∠ C' = γ' = 114.4433335428° = 114°26'36″ = 1.14441796434 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 = 24 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 24+29+29 = 82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 82 }{ 2 } = 41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41 * (41-24)(41-29)(41-29) } ; ; T = sqrt{ 100368 } = 316.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 316.81 }{ 24 } = 26.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 316.81 }{ 29 } = 21.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 316.81 }{ 29 } = 21.85 ; ;

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{ 24**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 48° 53'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 65° 33'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-24**2-29**2 }{ 2 * 29 * 24 } ) = 65° 33'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 316.81 }{ 41 } = 7.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 48° 53'12" } = 15.93 ; ;




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