11 24 25 triangle

Acute scalene triangle.

Sides: a = 11   b = 24   c = 25

Area: T = 130.7676968306
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ B = β = 71.99655469999° = 71°59'44″ = 1.25765593419 rad
Angle ∠ C = γ = 82.16325202369° = 82°9'45″ = 1.43440064999 rad

Height: ha = 23.77658124193
Height: hb = 10.89772473589
Height: hc = 10.46113574645

Median: ma = 23.88799078725
Median: mb = 15.13327459504
Median: mc = 13.86554246239

Inradius: r = 4.35988989435
Circumradius: R = 12.61878653629

Vertex coordinates: A[25; 0] B[0; 0] C[3.4; 10.46113574645]
Centroid: CG[9.46766666667; 3.48771191548]
Coordinates of the circumscribed circle: U[12.5; 1.7210618004]
Coordinates of the inscribed circle: I[6; 4.35988989435]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ B' = β' = 108.0044453° = 108°16″ = 1.25765593419 rad
∠ C' = γ' = 97.83774797631° = 97°50'15″ = 1.43440064999 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 = 11 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 11+24+25 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-11)(30-24)(30-25) } ; ; T = sqrt{ 17100 } = 130.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 130.77 }{ 11 } = 23.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 130.77 }{ 24 } = 10.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 130.77 }{ 25 } = 10.46 ; ;

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{ 11**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 25° 50'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 71° 59'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-24**2 }{ 2 * 24 * 11 } ) = 82° 9'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 130.77 }{ 30 } = 4.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 25° 50'31" } = 12.62 ; ;




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