15 24 28 triangle

Acute scalene triangle.

Sides: a = 15   b = 24   c = 28

Area: T = 179.9549819394
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 32.38222322764° = 32°22'56″ = 0.56551765724 rad
Angle ∠ B = β = 58.97107104672° = 58°58'15″ = 1.02992330599 rad
Angle ∠ C = γ = 88.64770572564° = 88°38'49″ = 1.54771830213 rad

Height: ha = 23.99333092526
Height: hb = 14.99658182828
Height: hc = 12.85435585282

Median: ma = 24.97549874875
Median: mb = 18.9876837546
Median: mc = 14.33003496461

Inradius: r = 5.37216363998
Circumradius: R = 14.00439040244

Vertex coordinates: A[28; 0] B[0; 0] C[7.73221428571; 12.85435585282]
Centroid: CG[11.91107142857; 4.28545195094]
Coordinates of the circumscribed circle: U[14; 0.33106477339]
Coordinates of the inscribed circle: I[9.5; 5.37216363998]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.6187767724° = 147°37'4″ = 0.56551765724 rad
∠ B' = β' = 121.0299289533° = 121°1'45″ = 1.02992330599 rad
∠ C' = γ' = 91.35329427436° = 91°21'11″ = 1.54771830213 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 = 15 ; ; b = 24 ; ; c = 28 ; ;

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

p = a+b+c = 15+24+28 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-15)(33.5-24)(33.5-28) } ; ; T = sqrt{ 32381.94 } = 179.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 179.95 }{ 15 } = 23.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 179.95 }{ 24 } = 15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 179.95 }{ 28 } = 12.85 ; ;

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{ 15**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 32° 22'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 58° 58'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-24**2 }{ 2 * 24 * 15 } ) = 88° 38'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 179.95 }{ 33.5 } = 5.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 32° 22'56" } = 14 ; ;




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