24 24 25 triangle

Acute isosceles triangle.

Sides: a = 24   b = 24   c = 25

Area: T = 256.0987515607
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 58.61218335357° = 58°36'43″ = 1.02329694758 rad
Angle ∠ B = β = 58.61218335357° = 58°36'43″ = 1.02329694758 rad
Angle ∠ C = γ = 62.77663329287° = 62°46'35″ = 1.09656537019 rad

Height: ha = 21.34114596339
Height: hb = 21.34114596339
Height: hc = 20.48878012485

Median: ma = 21.36658606192
Median: mb = 21.36658606192
Median: mc = 20.48878012485

Inradius: r = 7.01663702906
Circumradius: R = 14.05771453474

Vertex coordinates: A[25; 0] B[0; 0] C[12.5; 20.48878012485]
Centroid: CG[12.5; 6.82992670828]
Coordinates of the circumscribed circle: U[12.5; 6.43106559011]
Coordinates of the inscribed circle: I[12.5; 7.01663702906]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.3888166464° = 121°23'17″ = 1.02329694758 rad
∠ B' = β' = 121.3888166464° = 121°23'17″ = 1.02329694758 rad
∠ C' = γ' = 117.2243667071° = 117°13'25″ = 1.09656537019 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 = 25 ; ;

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

p = a+b+c = 24+24+25 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-24)(36.5-24)(36.5-25) } ; ; T = sqrt{ 65585.94 } = 256.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 256.1 }{ 24 } = 21.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 256.1 }{ 24 } = 21.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 256.1 }{ 25 } = 20.49 ; ;

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**2-25**2 }{ 2 * 24 * 25 } ) = 58° 36'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 58° 36'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 62° 46'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 256.1 }{ 36.5 } = 7.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 58° 36'43" } = 14.06 ; ;




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