24 25 29 triangle

Acute scalene triangle.

Sides: a = 24   b = 25   c = 29

Area: T = 286.1821760425
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 52.13657227104° = 52°8'9″ = 0.91099400192 rad
Angle ∠ B = β = 55.32218804133° = 55°19'19″ = 0.96655489616 rad
Angle ∠ C = γ = 72.54223968763° = 72°32'33″ = 1.26661036728 rad

Height: ha = 23.84884800354
Height: hb = 22.8954540834
Height: hc = 19.73766731328

Median: ma = 24.2699322199
Median: mb = 23.5
Median: mc = 19.75547462651

Inradius: r = 7.33879938571
Circumradius: R = 15.22001301325

Vertex coordinates: A[29; 0] B[0; 0] C[13.65551724138; 19.73766731328]
Centroid: CG[14.21883908046; 6.57988910443]
Coordinates of the circumscribed circle: U[14.5; 4.56600390397]
Coordinates of the inscribed circle: I[14; 7.33879938571]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.864427729° = 127°51'51″ = 0.91099400192 rad
∠ B' = β' = 124.6788119587° = 124°40'41″ = 0.96655489616 rad
∠ C' = γ' = 107.4587603124° = 107°27'27″ = 1.26661036728 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 24+25+29 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-24)(39-25)(39-29) } ; ; T = sqrt{ 81900 } = 286.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 286.18 }{ 24 } = 23.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 286.18 }{ 25 } = 22.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 286.18 }{ 29 } = 19.74 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 52° 8'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 55° 19'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-24**2-25**2 }{ 2 * 25 * 24 } ) = 72° 32'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 286.18 }{ 39 } = 7.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 52° 8'9" } = 15.2 ; ;




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