24 25 28 triangle

Acute scalene triangle.

Sides: a = 24   b = 25   c = 28

Area: T = 281.3043994817
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 53.48773679008° = 53°29'15″ = 0.93435306781 rad
Angle ∠ B = β = 56.84771120714° = 56°50'50″ = 0.99221692759 rad
Angle ∠ C = γ = 69.66655200278° = 69°39'56″ = 1.21658926996 rad

Height: ha = 23.44219995681
Height: hb = 22.50443195854
Height: hc = 20.09331424869

Median: ma = 23.67548812035
Median: mb = 22.88655849827
Median: mc = 20.11221853611

Inradius: r = 7.3076597268
Circumradius: R = 14.93304669588

Vertex coordinates: A[28; 0] B[0; 0] C[13.125; 20.09331424869]
Centroid: CG[13.70883333333; 6.69877141623]
Coordinates of the circumscribed circle: U[14; 5.18883372682]
Coordinates of the inscribed circle: I[13.5; 7.3076597268]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.5132632099° = 126°30'45″ = 0.93435306781 rad
∠ B' = β' = 123.1532887929° = 123°9'10″ = 0.99221692759 rad
∠ C' = γ' = 110.3344479972° = 110°20'4″ = 1.21658926996 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 = 28 ; ;

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

p = a+b+c = 24+25+28 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-24)(38.5-25)(38.5-28) } ; ; T = sqrt{ 79131.94 } = 281.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 281.3 }{ 24 } = 23.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 281.3 }{ 25 } = 22.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 281.3 }{ 28 } = 20.09 ; ;

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**2-28**2 }{ 2 * 25 * 28 } ) = 53° 29'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 56° 50'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-24**2-25**2 }{ 2 * 25 * 24 } ) = 69° 39'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 281.3 }{ 38.5 } = 7.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 53° 29'15" } = 14.93 ; ;




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