24 24 28 triangle

Acute isosceles triangle.

Sides: a = 24   b = 24   c = 28

Area: T = 272.9110241655
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 71.37106694253° = 71°22'14″ = 1.24656531708 rad

Height: ha = 22.74325201379
Height: hb = 22.74325201379
Height: hc = 19.49435886896

Median: ma = 23.15216738056
Median: mb = 23.15216738056
Median: mc = 19.49435886896

Inradius: r = 7.18218484646
Circumradius: R = 14.774408827

Vertex coordinates: A[28; 0] B[0; 0] C[14; 19.49435886896]
Centroid: CG[14; 6.49878628965]
Coordinates of the circumscribed circle: U[14; 4.72195004196]
Coordinates of the inscribed circle: I[14; 7.18218484646]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 108.6299330575° = 108°37'46″ = 1.24656531708 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 = 24 ; ; c = 28 ; ;

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

p = a+b+c = 24+24+28 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-24)(38-24)(38-28) } ; ; T = sqrt{ 74480 } = 272.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 272.91 }{ 24 } = 22.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 272.91 }{ 24 } = 22.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 272.91 }{ 28 } = 19.49 ; ;

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**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 54° 18'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 54° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 71° 22'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 272.91 }{ 38 } = 7.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 54° 18'53" } = 14.77 ; ;




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